Role of boundary conditions in the finite-size Ising model

1987/05/01 by G. G. Cabrera, R. Jullien · 3 citations
Physics and Astronomy · #Opinion Dynamics and Social Influence #Quantum many-body systems #Theoretical and Computational Physics

paper · doi:10.1103/physrevb.35.7062

openalex publication_date 1987/05/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/23

Abstract

Boundary conditions monitor the finite-size dependence of scaling functions for the Ising model. We study the low-temperature phase for the extremely anisotropic limit, or quantum version of the 2D classical Ising model, by means of combined exact results and large-size numerical calculations. The mass gap (inverse of correlation length) is the suitable order parameter for the finite system, and its finite-size behavior is studied as a function of variable boundary conditions. We find that the well-known exponential convergence to zero of the mass gap is only valid in a limited range of parameters; it strikingly changes into a power law for antiperiodic boundary conditions. We suggest that this puzzling phenomenon is associated with topological excitations.

Citations

• Order and disorder in gauge systems and magnets
• An introduction to lattice gauge theory and spin systems
• Two soluble models of an antiferromagnetic chain

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