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1989•Acta Physica SinicaOpen access

THE UPPER LIMIT OF CRITICAL TEMPERATURE OF N DIMENSIONAL ISING MODEL

LUAN CHANG-FU, 中山大学数学系

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Abstract

In the present article, by using coupling technique, we establish the relation between Ising model and contact process. From this relation, the upper limit of critical temperature of higher dimensional Ising model is obtained. That is, the critical point βc(n) of n-dimensional Ising model must satisfy exp{2βc(n)(2n-1)}·(exp{2βc(n)}-1)≥2/2n-1 and especially, crirical point βc(3) of the three-dimensional Ising model must satisfy βc(3)> 1/2ln1.17.

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What this paper is about

In the present article, by using coupling technique, we establish the relation between Ising model and contact process. From this relation, the upper limit of critical temperature of higher dimensional Ising model is obtained. That is, the critical point βc(n) of n-dimensional Ising model must satisfy exp{2βc(n)(2n-1)}·(exp{2βc(n)}-1)≥2/2n-1 and especially, crirical point βc(3) of the three-dimensional Ising model must satisfy βc(3)> 1/2ln1.17.

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Available abstract

In the present article, by using coupling technique, we establish the relation between Ising model and contact process. From this relation, the upper limit of critical temperature of higher dimensional Ising model is obtained. That is, the critical point βc(n) of n-dimensional Ising model must satisfy exp{2βc(n)(2n-1)}·(exp{2βc(n)}-1)≥2/2n-1 and especially, crirical point βc(3) of the three-dimensional Ising model must satisfy βc(3)> 1/2ln1.17.

Key concepts: Ising model, Square-lattice Ising model, Physics, Limit (mathematics), Critical point (mathematics), Coupling (piping), Statistical physics, Mathematical physics

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