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Updated finite temperature
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‎content/finitetemp/bccFe-Tsweep/Base/inpsd.dat‎

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simid bccFe100
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ncell 10 10 10 System size
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BC P P P Boundary conditions (0=vacuum, P=periodic)
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cell 1.00000 0.00000 0.00000
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0.00000 1.00000 0.00000
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0.00000 0.00000 1.00000
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Sym 1 Symmetry of lattice (0 for no, 1 for cubic, 2 for 2d cubic, 3 for hexagonal)
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posfile ./posfile
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momfile ./momfile
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exchange ./jfile
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SDEalgh 1 SDE solver: 1=midpoint, 2=heun, 3=heun3, 4=Heun_proper, 5=Depondt
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Initmag 1 Initial config of moments (1=random, 2=cone, 3=spec., 4=file)
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#restartfile ./restart.bccFe100.out
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Mensemble 5
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ip_mode M Initial phase parameters
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ip_temp TEMP --
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ip_mcNstep 10000 --
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!!mode H S=SD, M=MC
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!!temp TEMP Measurement phase parameters
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!!mcNstep 20000
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mode S S=SD, M=MC
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temp TEMP Measurement phase parameters
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Nstep 20000
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damping 0.1
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timestep 1.0e-16
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do_avrg Y Measure averages
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do_cumu Y
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cumu_step 50
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cumu_buff 10
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do_tottraj N Measure moments
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tottraj_step 1000
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plotenergy 1
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‎content/finitetemp/bccFe-Tsweep/Base/jfile‎

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1 1 0.5 0.5 0.5 1.33767484769984
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1 1 1.0 0.0 0.0 0.75703576545650
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1 1 1.0 1.0 0.0 -0.05975437643846
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1 1 1.5 0.5 0.5 -0.08819834160658

‎content/finitetemp/bccFe-Tsweep/Base/momfile‎

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1 1 2.23 1.0 0.0 0.0 2.0
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2 1 2.23 1.0 0.0 0.0 2.0

‎content/finitetemp/bccFe-Tsweep/Base/posfile‎

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1 1 0.000000 0.000000 0.000000
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2 1 0.500000 0.500000 0.500000

‎content/finitetemp/bccFe-Tsweep/README.txt‎

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Sweeps the bccFe over many temps
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1) ./runme.sh
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2) ./printM.sh
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3) gnuplot plot.gnu

‎content/finitetemp/bccFe-Tsweep/plot.gnu‎

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set xlabel "Temperature (K)"
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set xrange [0:1600]
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set yrange [0:1.1]
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p "thermal.norm.dat" u 1:2 w lp ti "Magnetization"
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rep "thermal.norm.dat" u 1:3 w lp ti "Binder cumulant"
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rep "thermal.norm.dat" u 1:4 w lp ti "Susceptibility"
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rep "thermal.norm.dat" u 1:5 w lp ti "Specific heat"
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pause(-1)
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set term png
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set output "bccfe.png"
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rep

‎content/finitetemp/bccFe-Tsweep/plotMT.py‎

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import numpy as np
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import matplotlib.pyplot as pp
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import matplotlib.colors as colors
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import matplotlib as mpl
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from matplotlib.collections import LineCollection
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pp.style.use('default')
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pp.rc("figure", facecolor="white")
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# Load the normalized phase diagram
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mt=np.genfromtxt("thermal.norm.dat")
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na=mt.shape
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#print(na)
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#Plot phase diagram
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fig_mt = pp.figure()
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ax1 = fig_mt.add_subplot(111)
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#ax1.set_title("Adiabatic magnon spectrum")
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ax1.set_xlabel('Temperature (K)')
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ax1.set_ylabel('Normalized observable')
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#ax1.set_xticks([])
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#for x in range(1,na[1]-1):
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# ax1.plot(mt[:,0],mt[:,x])
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ax1.plot(mt[:,0],mt[:,1],label='M')
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ax1.plot(mt[:,0],mt[:,2],label='U4')
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ax1.plot(mt[:,0],mt[:,3],label='Xi')
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ax1.plot(mt[:,0],mt[:,4],label='Cv')
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ax1.axis('tight')
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ax1.legend()
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pp.show()
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fig_mt.savefig('mt.png', format='png', dpi=200)

‎content/finitetemp/bccFe-Tsweep/printM.sh‎

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#! /bin/bash
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m_max=`tail -n1 T*/cumulants.*.out | grep E | awk '{ print $2 }' | sort -gr | head -1 `
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cv_max=`tail -n1 T*/cumulants.*.out | grep E | awk '{ print $7 }' | sort -gr | head -1 `
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#cv_max=1
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x_max=`tail -n1 T*/cumulants.*.out | grep E | awk '{ print $6 }' | sort -gr | head -1 `
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echo "# Temp. Mavg UBinder Susc. Cv" > thermal.dat
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echo "# Temp. Mavg UBinder Susc. Cv" > thermal.norm.dat
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for Temp in 100 200 300 400 500 600 700 800 900 950 1000 1100 1200 1300 1400 1500 1600
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do
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tail -1 T$Temp/cumulants.*.out | awk '{ printf "%6i %f %f %f %f\n", temp, $2,$5,$6,$7 }' temp=$Temp >> thermal.dat
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tail -1 T$Temp/cumulants.*.out | awk '{ printf "%6i %f %f %f %f\n", temp, $2/m_max,$5,$6/x_max,$7/cv_max }' m_max=$m_max x_max=$x_max cv_max=$cv_max temp=$Temp >> thermal.norm.dat
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done
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exit

‎content/finitetemp/bccFe-Tsweep/runme.sh‎

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#! /bin/bash
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for Temp in 100 200 300 400 500 600 700 800 900 950 1000 1100 1200 1300 1400 1500 1600
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do
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mkdir T$Temp/ 2>/dev/null
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echo "Temp: " $Temp
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cp Base/* T$Temp/
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cd T$Temp/
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sed -i "s/TEMP/$Temp/g" inpsd.dat
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if [ $Temp -ne 100 ]
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then
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sed -i "s/#restart/restart/" inpsd.dat
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cp ../restart.bccFe100.out .
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fi
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${SD_BINARY} > out.log
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cp restart.bccFe100.out ../
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cd ..
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done
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exit

‎content/finitetemp/finitetemp.rst‎

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Thermalization
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--------------
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In this exercise the thermalization rates in spin simulations will be investigated.
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In this exercise the thermalization rates in spin simulations will be investigated.
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The input files can be found in the directory ``finitetemp/SimpleCubic``.
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As mentioned in the lecture, thermalising the system before performing measurements is crucial for ensuring relevant results.
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Thermalising the system before performing measurements is crucial for ensuring relevant results.
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Here we will investigate this for a simple cubic model system.
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The initial ``inpsd.dat`` file looks as follows
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* Change the sign of the next-nearest neighbour and redo the study. Is the magnetization a good measurable for determining the thermalization now?
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Phase diagrams
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--------------
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Obtaining the M vs T relationship is probably the most common use case for Monte Carlo simulations on spin systems.
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In this exercise you can compare the MC functionalities of UppASD with a the ALPS package.
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The system in question is here the 2d square lattice with NN exchange couplings.
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To compare with other model implementations this example uses the ``aunits Y`` flag which sets the temperature unit to the exchange strength ``J`` instead of Kelvin.
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Phase diagram for bcc Fe
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^^^^^^^^^^^^^^^^^^^^^^^^
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Atomistic spin dynamics simulations with Langevin dynamics can be used to investigate
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the thermal properties of materials. In this exercise you will investigate how the
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magnetic order parameter, the heat capacity, the susceptibility depends on temperature.
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Input files and scripts for bcc Fe can be found in ``examples/PhaseDiagrams/bccFe-Tsweep``.
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The ``inpsd.dat`` will here look as follows (to start with). Note the **TEMP** entries for initial and measurement temperatures.
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.. literalinclude:: SquareLattice/Base/inpsd.dat
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.. literalinclude:: bccFe-Tsweep/Base/inpsd.dat
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and the ``posfile`` and ``momfile``, and ``jfile`` files looks as
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.. literalinclude:: SquareLattice/Base/posfile
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.. literalinclude:: SquareLattice/Base/momfile
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.. literalinclude:: SquareLattice/Base/jfile
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Again, note that with ``aunits Y`` the exchange interaction in ``jfile`` is not defined in ``mRy`` but in the dimensionless energy scale of ``J`` (which is not Joule either).
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.. literalinclude:: /Base/posfile
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.. literalinclude:: bccFe-Tsweep/Base/momfile
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.. literalinclude:: bccFe-Tsweep/Base/jfile
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In order to obtain the full M(T) curve, several simulations are needed at consecutive temperatures.
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This is preferably scripted, like in this example where we use a simple ``bash`` script ``runme.sh``
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.. literalinclude:: SquareLattice/runme.sh
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.. literalinclude:: bccFe-Tsweep/runme.sh
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Here you either need to replace the ``${SD_BINARY}`` expression, or export the location of your UppASD binary as the environment variable with the same name.
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You also need to use the same directory structure as intended, i.e. put the input files in a directory called `Base` and the ``runme.sh``
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script in the directory below.
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* Run the script and plot the resulting M(T) curve.
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* Run the sweep over temperature with the ``runme.sh`` script. What kind of simulations is run?
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* Examine the results by using the printM.sh and the plot.gnu scripts. The latter is a script for Gnuplot.
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* Change the inpsd.dat so that you can the temperature sweep as a Monte Carlo simulation, instead of an ASD simulation. Compare the results with each other, and with Fig. 2 of [Skubic2008]_.
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* Compare with the reference data in the :download:`sc_64_ALPS.dat <SquareLattice/sc_64_ALPS.dat>` file
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* Run additional simulations for different cell sizes. Use the Binder cumulant crossing approach to determine the critical temperature.
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* Are the simulation parameters "good enough" or are more thermalization/sampling steps needed to obtain an accurate M(T) curve?
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Minimization

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