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首页> 外文期刊>Physical review, E. Statistical physics, plasmas, fluids, and related interdisciplinary topics >Geometric properties of two-dimensional critical and tricritical Potts models
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Geometric properties of two-dimensional critical and tricritical Potts models

机译：二维临界和三临界Potts模型的几何性质

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摘要

We investigate geometric properties of the general q-state Potts model in two dimensions, and define geometric clusters as sets of lattice sites in the same Potts state, connected by nearest-neighbor bonds with variable probability p. We find that, besides the random-cluster fixed point, both the critical and the tricritical Potts models have another fixed point in the p direction. For the critical model, the random-cluster fixed point p(r) is unstable and the other point p(g)greater than or equal top(r) is stable; while p(r) is stable and p(g)less than or equal top(r) is unstable at tricriticality. Moreover, we show that the fixed point p(g) of a critical and tricritical q-state Potts models can be regarded to correspond to p(r) of a tricritical and critical q(')-state Potts models, respectively. In terms of the coupling constant of the Coulomb gas g, these two models are related as gg(')=16. By means of Monte Carlo simulations, we obtain p(g)=0.6227(2) and 0.6395(2) for the tricritical Blume-Capel and the q=3 Potts model, respectively, and confirm the predicted values of the magnetic and bond-dilution exponents near p(g).
机译：我们在二维中研究一般q状态Potts模型的几何特性，并将几何簇定义为相同Potts状态下的点阵集，并通过概率为p的最近邻键连接。我们发现，除了随机聚类固定点外，临界和三临界Potts模型在p方向上都具有另一个固定点。对于临界模型，随机簇固定点p（r）是不稳定的，而其他点p（g）大于或等于top（r）则是稳定的; p（r）是稳定的，而p（g）小于或等于top（r）在三临界状态下是不稳定的。此外，我们表明，临界和三临界q状态Potts模型的不动点p（g）可以分别视为对应于三临界和临界q（'）状态Potts模型的p（r）。就库仑气体g的耦合常数而言，这两个模型的关系为gg（'）= 16。借助蒙特卡洛模拟，我们分别针对三临界Blume-Capel模型和q = 3 Potts模型分别获得了p（g）= 0.6227（2）和0.6395（2），并确定了磁和键p（g）附近的稀释指数。

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