Transition temperature scaling in weakly coupled two-dimensional Ising models

Jordan C. Moodie, Manjinder Kainth, Matthew R. Robson and M.W. Long

Physica A: Statistical Mechanics and its Applications, 2020, vol. 541, issue C

Abstract: We investigate the proposal that for weakly coupled two-dimensional magnets the transition temperature scales with a critical exponent which is equivalent to that of the susceptibility in the underlying two-dimensional model, γ. Employing the exact diagonalization of transfer matrices we can determine the critical temperature for Ising models accurately and then fit to approximate this critical exponent. We find an additional logarithm is required to predict the transition temperature, stemming from the fact that the heat capacity exponent α tends to zero for this Ising model, complicating the elementary prediction. We suggest that the excitations of the transfer matrix correspond to thermalized topological excitations of the model and find that even the simplest model exhibits significant changes of behavior for the most relevant of these excitations as the temperature is varied.

Keywords: Bilayer Ising model; Scaling theory; Critical exponents; Transfer matrices (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119318369

DOI: 10.1016/j.physa.2019.123276

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