利用平均场边界严格分析非连续相变
Rigorous analysis of discontinuous phase transitions via mean-field bounds
摘要：
我们考虑定义在d维超立方晶格Z^d上的各种最近邻自旋模型。我们的基本假设是，这些模型满足反射积极性的条件。我们证明，每当相关的平均域论理论预测的不连续过渡，实际的模型也经历了不连续的过渡（发生在平均场转变温度附近），提供的尺寸是足够大的或在平均场模型的一阶过渡是足够强的。作为我们的一般理论的应用，我们证明了当d足够大时，Z^d上的三态Potts铁磁体随着温度的变化会发生一级相变。对于所有q态Potts模型（q>=3）、r分量立方模型（r>=4）和O（N）-双折射液晶模型（N>=3），都建立了类似的结果。
英文摘要：
We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice Z^d. Our essential assumption is that these models satisfy the condition of reflection positivity. We prove that whenever the associated mean-field theory predicts a discontinuous transition, the actual model also undergoes a discontinuous transition (which occurs near the mean-field transition temperature), provided the dimension is sufficiently large or the first-order transition in the mean-field model is sufficiently strong. As an application of our general theory, we show that for d sufficiently large, the 3-state Potts ferromagnet on Z^d undergoes a first-order phase transition as the temperature varies. Similar results are established for all q-state Potts models with q>=3, the r-component cubic models with r>=4 and the O(N)-nematic liquid-crystal models with N>=3.
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