Critical dynamics of random surfaces: Time evolution of area and genus

IF 3.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications Pub Date : 2025-09-09 DOI:10.1016/j.physa.2025.130959

Christof Schmidhuber

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引用次数: 0

Abstract

Conformal field theories with central charge

c \leq 1

on random surfaces have been extensively studied in the past. Here, this discussion is extended from their equilibrium distribution to their critical dynamics. This is motivated by the conjecture that these models describe the time evolution of certain social networks that are self-driven to a critical point. This paper focuses on the dynamics of the overall area and the genus of the surface. The time evolution of the area is shown to follow a Cox–Ingersoll–Ross process. Planar surfaces shrink, while higher genus surfaces grow to a size of order of the inverse cosmological constant. The time evolution of the genus is argued to lead to two different phases, dominated by (i) planar surfaces, and (ii) “foamy” surfaces, whose genus diverges. In phase (i), which exhibits critical phenomena, time variations of the order parameter are approximately t-distributed with 4 or more degrees of freedom.

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随机曲面的临界动力学：面积和属的时间演化

随机表面上中心电荷c≤1的共形场理论已经得到了广泛的研究。在这里，讨论从它们的平衡分布扩展到它们的临界动力学。这是基于这样一种猜想，即这些模型描述了某些自驱动到临界点的社交网络的时间演变。本文的重点是整体面积和表面属的动力学。该区域的时间演化遵循Cox-Ingersoll-Ross过程。平面会收缩，而更高的属面会增长到逆宇宙常数的数量级。该属的时间演化被认为导致了两个不同的阶段，由(i)平面表面和（ii）“泡沫”表面主导，其属发散。在表现出临界现象的阶段(i)中，序参量的时间变化近似为t分布，具有4个或更多的自由度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica A: Statistical Mechanics and its Applications 物理-物理：综合

CiteScore

7.20

自引率

9.10%

发文量

852

审稿时长

6.6 months

期刊介绍： Physica A: Statistical Mechanics and its Applications Recognized by the European Physical Society Physica A publishes research in the field of statistical mechanics and its applications. Statistical mechanics sets out to explain the behaviour of macroscopic systems by studying the statistical properties of their microscopic constituents. Applications of the techniques of statistical mechanics are widespread, and include: applications to physical systems such as solids, liquids and gases; applications to chemical and biological systems (colloids, interfaces, complex fluids, polymers and biopolymers, cell physics); and other interdisciplinary applications to for instance biological, economical and sociological systems.