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Journal of Statistical Theory and Practice

, Volume 5, Issue 3, pp 413–424 | Cite as

Simulation Reductions for the Ising Model

  • Mark Huber
Article

Abstract

Polynomial time reductions between problems have long been used to delineate problem classes, where an oracle for solving one problem yields a solution to another. Simulation reductions also exist, where an oracle for simulation from a probability distribution is employed in order to obtain draws from another distribution. Here linear time simulation reductions are given for: the Ising spins world to the Ising subgraphs world and the Ising subgraphs world to the Ising spins world. This answers a long standing question of whether such a direct relationship between these two versions of the Ising model existed. Moreover, these reductions result in the first method for perfect simulation from the subgraphs world and a new Swendsen-Wang style Markov chain for the Ising model. The method used is to write the desired distribution with set parameters as a mixture of distributions where the parameters are at their extreme values.

AMS Subject Classification

68U20 65C05 68Q25 

Key-words

Monte Carlo Simulation reduction Ising model High temperature expansion 

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Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  1. 1.Claremont McKenna CollegeClaremontUSA

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