Documentation:ClassicalMCSimulations

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ALPS application: spinmc

The spinmc package is one of the applications of the ALPS project. It provides a a generic implementation of local and cluster updates for classical spin systems.

The applications supports the following models on arbitrary lattices:

  • Ising models
  • XY models
  • Heisenberg models
  • 3-, 4- and 10-state Potts models

The application can easily be extended to additional q states Potts models and O(N) models by editing the file mc/spins/spinmc_factory.C in a straightforward manner.

Running a simulation

is discussed in the tutorial.

Input parameters

In addition to the general input parameters of the ALPS scheduler library the spinmc application takes the following input parameters:


NameDefaultDescription
LATTICE_LIBRARYlattices.xmlpath to a file containing lattice descriptions
LATTICEname of the lattice
MODELeither Ising, XY, Heisenberg or Potts
qthe number of different states in a Potts model
UPDATEthe update type, either local or cluster
ERROR_VARIABLEthe name of an observable whose error you would like ALPS to monitor (must be used with ERROR_LIMIT)
ERROR_LIMITonce ERROR_VARIABLE's absolute error is less than this amount, ALPS will stop the task (must be used with ERROR_VARIABLE)
Tthe temperature
Jthe default coupling constant
J#Jthe coupling constant on a bond with type # (#=0,1,...).
Donsite single-ion anisotropy coupling constants (one for each spin component in a list, e.g. D="0.0 0.0 10.0")
CONVENTIONclassicalspecifies whether the classical or quantum conventions are used (see below)
S1 if CONVENTION=classical
1/2 if CONVENTION=quantum
the default spin size
S#Sthe spin size on a site with type # (#=0,1,...).
g1the Landee g-factor, used for suscpetibility measurements
h0external magnetic field (only with local update)

In addition, the lattice description can require further parameters (e.g. L or W) as specified in the lattice description file.

Note: while the classical Monte carlo program uses XML lattice description it does not use XML model descriptions. The model is instead specifiec by the parameters in the table above.

Local versus cluster updates

Cluster updates should be used as long as there is no magnetic field applied and the spin system is not frustrated. Otherwise local updates are preferred.

Quantum versus classical conventions

Quantum and classical spin models often use different conventions for the coupling constants, and the CONVENTION parameter allows to choose between the two.

  • classical convention is to have positive signs denote ferromagnetic coupling. The coupling strengths are multiplied by S2 if a parameter S is specified.
  • quantum convention is to have positive signs denote anti-ferromagnetic coupling. The coupling strengths are multiplied by S(S+1) where S defaults to 1/2.

Measurements

The following observables are measured by the spinmc application:

NameDescription
Energythe total energy of the system
Energy Densitythe energy density (energy per site) of the system
Specific Heatthe specific heat per site of the system
Magnetizationthe z-component of the magnetization
|Magnetization|absolute value of the z-component of the magnetization
Magnetization^2square of the z-component of the magnetization
Magnetization along Fieldthe component of the magnetization along the external magnetic field
Staggered Magnetizationthe z-component of the staggered magnetization (only on bipartite lattices)
Staggered Magnetization^2square of the z-component of the staggered magnetization (only on bipartite lattices)
Susceptibilitythe uniform susceptibility, includes a factor of g2
Cluster sizethe mean cluster size as a fraction of the lattice volume (only for cluster updates)

Note: To evaluate the specific heat the evaluation program spinmc_evaluate has to be run on the task files (*task*.xml).

License

The license allows the use of the applications for non-commercial scientific use provided that the use of the ALPS applications and libraries is acknowledged and referenced in any scientific publication, as discussed in this license file.

Questions and request for support

can be addressed to Matthias Troyer.

Contributions and feature requests

We appreciate hearing your requests for additional features and also welcome any contributions to the ALPS project.

Contributors

The following persons have contributed to the classical spins application:


copyright (c) 2002-2004 by Matthias Troyer