变形Cauchy随机矩阵系综与大$N$相变
Deformed Cauchy random matrix ensembles and large $N$ phase transitions
摘要：
本文研究了一个新的厄米单矩阵模型，它包含一个对数Penner型项和另一个项，后者可以作为对数项的极限而得到。对于小耦合，电势在原点处具有绝对最小值，但是超过一定的耦合值，电势发展为双阱。对于较高的耦合临界值，系统经历了一个大的$N$三阶相变。
英文摘要：
We study a new hermitian one-matrix model containing a logarithmic Penner's type term and another term, which can be obtained as a limit from logarithmic terms. For small coupling, the potential has an absolute minimum at the origin, but beyond a certain value of the coupling the potential develops a double well. For a higher critical value of the coupling, the system undergoes a large $N$ third-order phase transition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
