二维经典和一维量子伊辛模型的 Kac-Ward 解法

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL Annales Henri Poincaré Pub Date : 2024-09-09 DOI:10.1007/s00023-024-01479-2

Georgios Athanasopoulos, Daniel Ueltschi

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引用次数: 0

摘要

我们严格推导了 (i) 三角晶格上具有平移不变耦合常数的经典伊辛模型和 (ii) 一维量子伊辛模型的自由能。我们采用了 Kac 和 Ward 的方法。新颖之处在于耦合常数可以是负号。我们描述了经典模型比热的对数奇异性和临界温度 Cimasoni-Duminil-Copin-Li 公式的有效性。我们还讨论了量子模型的量子相变。

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Kac–Ward Solution of the 2D Classical and 1D Quantum Ising Models

We give a rigorous derivation of the free energy of (i) the classical Ising model on the triangular lattice with translation-invariant coupling constants and (ii) the one-dimensional quantum Ising model. We use the method of Kac and Ward. The novel aspect is that the coupling constants may have negative signs. We describe the logarithmic singularity of the specific heat of the classical model and the validity of the Cimasoni–Duminil-Copin–Li formula for the critical temperature. We also discuss the quantum phase transition of the quantum model.

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.