硬平方模型的张量网络研究
Tensor network investigation of the hard-square model
摘要：
利用角转移矩阵重整化群收缩描述其配分函数的张量网络，我们研究了硬平方模型的相变的性质.硬平方模型是统计物理学中精确求解的模型之一，Baxter为它找到了一个可积流形.动机有两个方面：评估这种模型的张量网络的能力，并探测最近在里德伯原子链实验中引起极大关注的硬核玻色子的一维量子模型的二维经典模拟。因此，我们集中在两个平面上的三维参数空间跨越的活动和耦合常数在两个对角线方向。我们首先研究的唯一情况下，到目前为止，与蒙特卡罗模拟，相反的耦合常数的情况下研究。我们确认，远离和不太远的可积的3-状态Potts点，过渡期-3阶段似乎是唯一的胡斯-费舍尔手征普适性类，尽管显着不同的指数相比，蒙特卡罗。我们还确定了两个额外的相变没有报告到目前为止，该模型，一个Lifshitz无序线，和伊辛过渡足够大的活动。为了与里德伯原子的一维量子模型联系起来，我们转向一个铁磁耦合保持固定的平面，我们表明所得的相图非常相似，唯一的区别是伊辛跃迁通过三临界伊辛点变为一阶，与巴克斯特的预测一致，该平面应该包含三临界伊辛点，值得注意的是，几乎定量协议的相图的1D量子版本的模型。
英文摘要：
Using the corner-transfer matrix renormalization group to contract the tensor network that describes its partition function, we investigate the nature of the phase transitions of the hard-square model, one of the exactly solved models of statistical physics for which Baxter has found an integrable manifold. The motivation is twofold: assess the power of tensor networks for such models, and probe the 2D classical analog of a 1D quantum model of hard-core bosons that has recently attracted significant attention in the context of experiments on chains of Rydberg atoms. Accordingly, we concentrate on two planes in the 3D parameter space spanned by the activity and the coupling constants in the two diagonal directions. We first investigate the only case studied so far with Monte Carlo simulations, the case of opposite coupling constants. We confirm that, away and not too far from the integrable 3-state Potts point, the transition out of the period-3 phase appears to be unique in the Huse-Fisher chiral universality class, albeit with significantly different exponents as compared to Monte Carlo. We also identify two additional phase transitions not reported so far for that model, a Lifshitz disorder line, and an Ising transition for large enough activity. To make contact with 1D quantum models of Rydberg atoms, we then turn to a plane where the ferromagnetic coupling is kept fixed, and we show that the resulting phase diagram is very similar, the only difference being that the Ising transition becomes first-order through a tricritical Ising point, in agreement with Baxter's prediction that this plane should contain a tricritical Ising point, and in remarkable, almost quantitative agreement with the phase diagram of the 1D quantum version of the model.
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