The Ising model on tetrahedron-like lattices: a finite-size analysis

1993/07/27 by Oscar Diego, O. Diego, J. Gonzalez +3 · 1 citation
Mathematics · Physics and Astronomy · #Opinion Dynamics and Social Influence #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #hep-lat #hep-th

paper · pdf · doi:10.1088/0305-4470/27/9/013

published as J.Phys. A27 (1994) 2965-2983 · 25 pages + 6 figures not included. Latex file. FTUAM 93-27

arxiv created 1993/07/27 · openalex publication_date 1994/05/07 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We study, using dimer and Monte Carlo approaches, the critical properties and finite-size effects of the Ising model on honeycomb lattices folded on the tetrahedron. We show that the main critical exponents are not affected by the presence of conical singularities. The finite-size scaling of the position of the maxima of the specific heat does not match, however, with the scaling of the correlation length, and the thermodynamic limit is attained faster on the spherical surface than in corresponding lattices on the torus.

Citations

• Exact Finite Size Results on the Ising Model in 2D Curved Space
• Conformal invariance and universality in finite-size scaling
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• A comparative study of some pseudorandom number generators

Cited by

• Exact finite-size scaling with corrections in the two-dimensional Ising model with special boundary conditions