聖塔非研究所

關於玻爾茲曼-吉布斯統計力學中臨界現象理論中出現的數學分歧

2025-10-01 · 已發表論文 · 更新 2026/08/30 下午12:48

摘要 The standard Theory of Critical Phenomena within Boltzmann Gibbs 統計 mechanics is known to successfully predict, at any temperature differing from a continuous phase transition critical on…

本頁只刊出中文翻譯與中文說明;英文原文請見下方原文連結。

原文連結

論文資訊

  • 類型:已發表論文
  • 日期:2025-10-01

摘要

The standard Theory of Critical Phenomena within Boltzmann-Gibbs 統計 mechanics is known to successfully predict, at any temperature differing from a continuous-phase-transition critical one, the (finite) values for 熱力學ally relevant quantities such as isothermal magnetic susceptibility, specific heat, correlation length, Grüneisen parameter, and similar ones. However, at the precise critical point, empirically unreachable infinities emerge within that approach at the N -> infinity 熱力學al limit. Such divergences, although 數學ly correct, may be seen as poorly informative ones. Indeed, they make no distinction at all between say the Ising, XY, Heisenberg, and other models. Moreover, for say the XY model, they make no distinction whether the spins are, for instance, 1/2, 1 or 3/2, or whether the i

※ 此為已發表論文,全文需透過期刊付費取得