Exact treatment of Ising model on the helical tori
Tsong-Ming Liaw, Ming-Chang Huang, Yen-Liang Chou, Simon C. Lin and, Feng-Yin Li
TL;DR
This paper derives exact partition functions for the 2D Ising model on square lattices with helical boundary conditions, revealing that finite size effects do not depend on chirality.
Contribution
It provides exact closed-form solutions for the Ising model on helical tori and clarifies their relation to twisted boundary conditions via SL(2,Z) transformations.
Findings
Finite size effects are independent of chirality.
Exact partition functions are obtained for helical tori.
Helical boundary conditions relate to twisted boundary conditions through SL(2,Z).
Abstract
The exact closed forms of the partition functions of 2D Ising model on square lattices with twisted boundary conditions are given. The constructions of helical tori are unambiguously related to the twisted boundary conditions by virtue of the SL(2,Z) transforms. Numerical analyses reveal that the finite size effect is irrelevant to the chirality equipped with each helical boundary condition.
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Taxonomy
TopicsQuantum many-body systems · Physics of Superconductivity and Magnetism · Opinion Dynamics and Social Influence