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Exact algorithm for sampling the two-dimensional Ising spin glass.

Creighton K Thomas¹, A Alan Middleton

¹Department of Physics, Syracuse University, Syracuse, New York 13244, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2009

Summary

This summary is machine-generated.

A new algorithm efficiently generates spin-glass configurations for the Edwards-Anderson Ising model. This method overcomes slow simulation dynamics, enabling studies of long-range correlations and coarse-grained dynamics.

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Area of Science:

Statistical Mechanics
Computational Physics
Condensed Matter Physics

Background:

Direct simulation of spin-glass models like the 2D Edwards-Anderson Ising model is computationally intensive due to slow dynamics.
Studying long-range correlation functions and coarse-grained dynamics requires efficient sampling methods.

Purpose of the Study:

To develop a novel sampling algorithm for generating spin-glass configurations with probabilities proportional to their Boltzmann weights.
To overcome the limitations of direct simulation for studying complex spin-glass systems.

Main Methods:

The algorithm adapts Wilson's algorithm for sampling dimer coverings on related graphs.
It employs a recursive approach, dividing the sample and computing probabilities along a separator.
Pfaffian elimination is used for sampling dimer configurations, offering efficiency over Gaussian elimination.

Main Results:

The algorithm achieves an asymptotic run-time of O(n(3/2)) for n spins.
Required floating-point precision scales inversely with temperature and slowly with system size.
Benchmarking results are presented for system sizes up to n=128(2) with various boundary conditions.

Conclusions:

The developed algorithm provides an efficient method for sampling spin-glass configurations, significantly improving upon direct simulation.
It enables more effective studies of critical phenomena and dynamics in spin-glass systems.
The algorithm's efficiency and scalability make it suitable for large-scale simulations.