Updated examples for finite temperature exercises.

aibergman · aibergman · commit a9d856d4057b · 2022-10-12T09:02:21.000+02:00
diff --git a/content/finitetemp/ChiralSpiral/dmfile b/content/finitetemp/ChiralSpiral/dmfile
@@ -0,0 +1,4 @@
+1 1  1.0000  0.0000 0.0000  0.81650  0.00000  0.00000
+1 1 -1.0000  0.0000 0.0000 -0.81650 -0.00000 -0.00000
+1 1  0.0000  1.0000 0.0000  0.00000  0.81650  0.00000
+1 1  0.0000 -1.0000 0.0000 -0.00000 -0.81650 -0.00000
diff --git a/content/finitetemp/ChiralSpiral/gs.png b/content/finitetemp/ChiralSpiral/gs.png
diff --git a/content/finitetemp/ChiralSpiral/inpsd.dat b/content/finitetemp/ChiralSpiral/inpsd.dat
@@ -0,0 +1,29 @@
+simid SCsurf_T
+ncell     128 128 1
+BC        P         P         0                 Boundary conditions (0=vacuum,P=periodic)
+cell      1.00000   0.00000   0.00000 
+          0.00000   1.00000   0.00000
+          0.00000   0.00000   1.00000
+
+do_prnstruct 2
+posfile   ./posfile
+exchange  ./jfile
+momfie    ./momfile
+dm        ./dmfile
+
+
+Initmag   1                                     (1=random, 2=cone, 3=spec., 4=file)
+
+ip_mode N
+ip_mcanneal 0
+
+mode      S                                     M for MC and S for SD
+temp      0.000
+damping   0.500
+Nstep     5000
+timestep  1.000e-15       s                    The time step-size for the SDE-solver
+
+
+plotenergy   1   
+do_avrg      Y
+do_cumu      Y
diff --git a/content/finitetemp/ChiralSpiral/jfile b/content/finitetemp/ChiralSpiral/jfile
@@ -0,0 +1,4 @@
+1 1  1.0       0.0       0.0      1.00000
+1 1 -1.0       0.0       0.0      1.00000
+1 1  0.0       1.0       0.0      1.00000
+1 1  0.0      -1.0       0.0      1.00000
diff --git a/content/finitetemp/ChiralSpiral/momfile b/content/finitetemp/ChiralSpiral/momfile
@@ -0,0 +1 @@
+1 1 1.0 0.1 0.0 1.0 
diff --git a/content/finitetemp/ChiralSpiral/posfile b/content/finitetemp/ChiralSpiral/posfile
@@ -0,0 +1 @@
+1 1 0.0 0.0 0.0
diff --git a/content/finitetemp/SquareAniLattice/inpsd.dat b/content/finitetemp/SquareAniLattice/inpsd.dat
@@ -0,0 +1,34 @@
+simid  SquareKz 
+ncell     64 64 1
+BC        P         P         0                 Boundary conditions (0=vacuum,P=periodic)
+cell      1.00000   0.00000   0.00000
+          0.00000   1.00000   0.00000
+          0.00000   0.00000   1.00000
+Sym       1                                     Symmetry of lattice (0 for no, 1 for cubic, 2 for 2d cubic, 3 for hexagonal)
+
+aunits Y
+posfile    ./posfile
+exchange   ./jfile
+momfile    ./momfile
+anisotropy ./kfile
+do_prnstruct 1
+
+Mensemble 1
+Initmag   3                                     (1=random, 2=cone, 3=spec., 4=file)
+#restartfile ./restart
+
+ip_mode   M                                     Initial phase parameters
+ip_temp   0.001                                 --
+ip_mcNstep     3000                            --
+
+mode      M                                     S=SD, M=MC
+temp      0.001                                 Measurement phase parameters
+mcNstep   2000                                --
+#Nstep    10000                                --
+#damping  0.5
+#timestep 1
+
+do_avrg   Y                                     Measure averages
+do_tottraj Y                                    Measure moments
+plotenergy 1                                    Calculate energy 
+do_cumu Y                                       Calculate cumulants
diff --git a/content/finitetemp/SquareAniLattice/jfile b/content/finitetemp/SquareAniLattice/jfile
@@ -0,0 +1 @@
+ 1 1    1.0    0.0    0.0    0.5000
diff --git a/content/finitetemp/SquareAniLattice/kfile b/content/finitetemp/SquareAniLattice/kfile
@@ -0,0 +1 @@
+1 1 -0.40   0.00   0.00000   0.00000   1.00000  0.0
diff --git a/content/finitetemp/SquareAniLattice/mcanneal.snippet b/content/finitetemp/SquareAniLattice/mcanneal.snippet
@@ -0,0 +1,7 @@
+ip_mode H
+ip_mcanneal 5
+1000 2.0
+1000 0.5
+1000 0.1
+1000 0.01
+1000 0.001
diff --git a/content/finitetemp/SquareAniLattice/momfile b/content/finitetemp/SquareAniLattice/momfile
@@ -0,0 +1 @@
+1 1 1.00000 0.0 0.0 1.0
diff --git a/content/finitetemp/SquareAniLattice/posfile b/content/finitetemp/SquareAniLattice/posfile
@@ -0,0 +1 @@
+1   1   0.0 0.0 0.0                    
diff --git a/content/finitetemp/finitetemp.rst b/content/finitetemp/finitetemp.rst
@@ -72,14 +72,16 @@ and the ``posfile`` and ``momfile``, and ``jfile`` files looks as
 .. literalinclude:: SquareLattice/Base/momfile
 .. literalinclude:: SquareLattice/Base/jfile
 
-Again, note that with ``aunits Y`` the exchange interaction in ``jfile`` is not defined in ``mRy`` but in the dimensionless energy scale of ``J`` (not Joule either).
+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).
 
 In order to obtain the full M(T) curve, several simulations are needed at consecutive temperatures. 
 This is preferably scripted, like in this example where we use a simple ``bash`` script ``runme.sh``
 
 .. literalinclude:: SquareLattice/runme.sh
 
 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.
+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``
+script in the directory below. 
 
  * Run the script and plot the resulting M(T) curve. 
 
@@ -90,3 +92,82 @@ Here you either need to replace the ``${SD_BINARY}`` expression, or export the l
 
 Minimization
 ------------
+
+Ground state determination is another situation where Monte Carlo and Atomistic spin dynamics simulations are used extensively. 
+For isotropic ferromagnets this is usually a trivial task but for systems with exchange frustration and/or strongly anisotropic systems
+the ground state search can prove quite demanding.
+
+In this exercise you will examine different kinds of magnetic systems with the task of finding their respective ground states.
+
+Anisotropic systems
+^^^^^^^^^^^^^^^^^^^
+
+The first example starts from the square lattice of the previous exercise, but this time we will add a uniaxial anisotropy to the system.
+Copy the input files from the previous exercise and add a uniaxial anisotropy with a strength of ``0.4J`` , where ``J`` still is the 
+dimensionles unit of energy as earlier. An anisotropy is added by including the keyword ``anisotropy ./kfile`` to ``inpsd.dat`` and
+creating the anisotropy file ``kfile`` as per below. Also start with the ``jfile`` that only had positive exchange couplings.
+
+.. literalinclude:: SquareAniLattice/kfile
+
+Note that you can give all input files besides ``inpsd.dat`` more descriptive names if wanted.
+
+ * With the anisotropy included, simulate the system starting from the ferromagnetic configuration by using ``initmag 3`` and relax the system to a temperature approaching zero. You can visualize the structure using the GUI, or if it fails to run with the ``ASD_Tools/myRestart3.py`` script provided in the Github repository. :download:`< myRestart3.py <https://raw.githubusercontent.com/UppASD/UppASD/master/ASD_Tools/myRestart3.py>`
+
+This should give you a ferromagnetic order of the full sample, as expected. 
+
+ * Now change the starting guess to a fully disordered state by using ``initmag 1`` and redo the relaxation. What state do you end up with?
+
+The anisotropies in the system causes large energy barriers that can not be overcome at low temperatures.
+So unless the starting guess is good there is a risk that one ends up in a local minimum instead of the global one.
+To overcome these barriers one can employ higher temperatures which is typically done with the "Simulated annealing" (SA) approach, 
+where one performs consecutive initial phase runs, starting from a high temperature and gradually reducing the temperature to the target value.
+
+In UppASD, this is preferably done using the ``ip_mcanneal`` or ``ip_nphase`` constructs. An example is seen below.
+
+.. literalinclude:: SquareAniLattice/mcanneal.snippet
+
+There are no global recipies for the optimal number if anneal sweeps and the temperature distibution so here empirical experience is your friend.
+
+ * Try different SA sequences and see if you can relax the anisotropic system to its ferromagnetic ground state.
+
+Dzyalosinskii-Moriya systems
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Also without anisotropy, ground state relaxation can prove a formidable task.
+
+.. literalinclude:: ChiralSpiral/inpsd.dat
+
+and the ``posfile``, ``jfile``, ``momfile`` as below
+
+.. literalinclude:: ChiralSpiral/posfile
+.. literalinclude:: ChiralSpiral/jfile
+.. literalinclude:: ChiralSpiral/momfile
+
+Now we also have a Dzyaloshinskii-Moriya (DM) file ``dmfile`` that looks like 
+
+.. literalinclude:: ChiralSpiral/dmfile
+
+where the first five columns are the same as for a regular ``jfile`` i.e. atom sites and distance vector :math:`\mathbf{R}_{ij}`. 
+The remaining three columns define the DM interaction vector :math:`\mathbf{D}_{ij}`. This system with ferromagnetic exchange and significant
+DM interactions has a spin-spiral ground state as shown below.
+
+.. figure:: ChiralSpiral/gs.png
+
+Fig. 1 Spin spiral ground state for a DM system.
+
+ * For this setup, start from a random configuration with ``initmag 1`` and relax the structure. What end state do you get?
+ 
+ * If you do not get the spiral state, try to obtain it with simulated annealing. How close can you come? Is the energy stabilizing?
+
+
+### Glassy systems
+### ^^^^^^^^^^^^^^
+### 
+### As a final challenge, lets consider a spin glass system. 
+### A simple yet illustrative model for a spin glass system is given by the Edwards-Anderson model, where a nearest neighbour Hamiltonian on a cubic 
+### lattice, but with random exchange interactions are used. 
+### 
+### #.. math::
+### #H=-\sum_{i,j} J_{ij}  \mathbf{m}_i \mathbf{m}_j
+### 
+### The UppASD code can model Edwards-Anderson spin glasses by the keywords

Original file line number	Diff line number	Diff line change
`@@ -0,0 +1 @@`
	`1`	`+1 1 -0.40 0.00 0.00000 0.00000 1.00000 0.0`