Exact Numerical Evaluations for Two-Dimensional Ising Models with Arbitrary Bond Configurations

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概要

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• An algorithm to make exact numerical evaluations for finite-size two-dimensional Ising models with arbitrary bond configurations under the toroidal periodic boundary condition is proposed. The algorithm is based on a modified version of the Cholesky-like factorization (MCLF) method and columnwise matrix inversions of very sparse skew-symmetric matrices. This enables us to exactly evaluate the internal energy, the specific heat and the entropy without use of any numerical differentiation. It also provides a general method to get the numerical value of a Pfaffian with its sign. The amount of memory and the CPU time required to get a result is measured to be proportional to N^<1.5∿1.8> and N^<2.4∿2.8>, respectively, where N is the number of the spins. As a demonstration we show temperature dependencies of the specific heat and the internal energy along the Nishimori line for±J models on lattices with sizes 25×25, 50×50 and 100×100, and we know the performance achieved is very high. Size-dependent anomalous behaviors cannot be seen in the result for the specific heat.

• 理論物理学刊行会の論文
• 2005-04-30

著者

• Tamaribuchi Tsuguhiro

  Department Of Physics Faculty Of Science Shizuoka University

関連論文

• Exactness of the Replica Method and Critical Renormalization on a Generalized Gaussian Model with Randomness
• Exact Numerical Evaluations for Two-Dimensional Ising Models with Arbitrary Bond Configurations

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