随机稀释三角形元胞模型：动力学约束下相变的研究
The Random-Diluted Triangular Plaquette Model: study of phase transitions in a Kinetically Constrained Model
摘要：
我们研究了三角元模型（TPM）的热力学性质如何受到额外相互作用的影响。原始TPM的热力学是微不足道的，而它的动力学是玻璃态的，就像在动力学约束模型中一样。一旦我们将模型推广到包括额外的相互作用，系统中就会出现热力学相变。我们考虑的附加相互作用要么是在平面上形成规则晶格的短程相互作用，要么是小世界类型的长程相互作用。在长程相互作用的情况下，我们称新模型为随机稀释TPM。我们提供的参数，这样修改的模型应该经历一个热力学相变，在长程的情况下，这是一个玻璃化转变的“随机一阶”的种类。最后，我们支持了我们在Bethe近似下研究随机稀释TPM有限温度相图的理论。这对应于随机规则图上的精确计算，其中自由能和构型熵可以通过腔方程来计算。
英文摘要：
We study how the thermodynamic properties of the Triangular Plaquette Model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in Kinetically Constrained Models. As soon as we generalize the model to include additional interactions, a thermodynamic phase transition appears in the system. The additional interactions we consider are either short ranged, forming a regular lattice in the plane, or long ranged of the small-world kind. In the case of long-range interactions we call the new model Random-Diluted TPM. We provide arguments that the model so modified should undergo a thermodynamic phase transition, and that in the long-range case this is a glass transition of the "Random First-Order" kind. Finally, we give support to our conjectures studying the finite temperature phase diagram of the Random-Diluted TPM in the Bethe approximation. This corresponds to the exact calculation on the random regular graph, where free-energy and configurational entropy can be computed by means of the cavity equations.
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