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首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >Potts models with (17) invisible states on thin graphs
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Potts models with (17) invisible states on thin graphs

机译：薄图上具有（17）不可见状态的Potts模型

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The order of a phase transition is usually determined by the nature of the symmetry breaking at the phase transition point and the dimension of the model under consideration. For instance, q-state Potts models in two dimensions display a second order, continuous transition for q = 2, 3, 4 and first order for higher q. Tamura et al recently introduced Potts models with 'invisible' states which contribute to the entropy but not the internal energy and noted that adding such invisible states could transmute continuous transitions into first order transitions (Tamura et al 2010 Prog. Theor. Phys. 124 381; 2011 J. Phys: Conf. Ser. 297 012022; 2012 Interface Between Quantum Information and Statistical Physics; Tanaka and Tamura 2011 J. Phys.: Conf. Ser. 320 012025). This was observed both in a Bragg-Williams type mean-field calculation and 2D Monte-Carlo simulations. It was suggested that the invisible state mechanism for transmuting the order of a transition might play a role where transition orders inconsistent with the usual scheme had been observed. In this paper we note that an alternative mean-field approach employing 3-regular random ('thin') graphs also displays this change in the order of the transition as the number of invisible states is varied, although the number of states required to effect the transmutation, 17 invisible states when there are 2 visible states, is much higher than in the Bragg-Williams case. The calculation proceeds by using the equivalence of the Potts model with two visible and r invisible states to the Blume-Emery-Griffiths (BEG) model, so a by-product is the solution of the BEG model on thin random graphs.
机译：相变的顺序通常取决于在相变点处对称性破坏的性质以及所考虑模型的尺寸。例如，二维的q状态Potts模型显示一个二阶，即q = 2、3、4的连续过渡，以及一个较高q的一阶。田村（Tamura）等人最近介绍了具有“不可见”状态的Potts模型，这些状态有助于熵，但对内部能量没有贡献，并指出添加这种不可见状态可能会将连续跃迁转变为一阶跃迁（Tamura等人2010 Prog。Theor。Phys。124381 ; 2011 J. Phys：Conf。Ser。297 012022; 2012量子信息与统计物理之间的接口; Tanaka和Tamura 2011 J. Phys .: Conf。Ser。320 012025）。在Bragg-Williams型平均场计算和2D蒙特卡洛模拟中都可以观察到这一点。有人提出，在已经观察到与常规方案不一致的过渡顺序的情况下，用于改变过渡顺序的不可见状态机制可能会发挥作用。在本文中，我们注意到，使用3个规则的随机（“细”）图的均值场方法也显示了这种转变的变化顺序，即随着不可见状态数的变化，尽管影响效果所需的状态数当存在2个可见状态时，,变即17个不可见状态要比布拉格-威廉斯案例高得多。通过使用具有两个可见状态和r不可见状态的Potts模型与Blume-Emery-Griffiths（BEG）模型的等价进行计算，因此，副产品是BEG模型在细随机图上的解决方案。

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