Eur. Phys. J. B (2017) 90: 245
https://doi.org/10.1140/epjb/e2017-80471-2

Regular Article

First-order transitions and thermodynamic properties in the 2D Blume-Capel model: the transfer-matrix method revisited

Department of Physics and Photon Science, School of Physics and Chemistry, Gwangju Institute of Science and Technology, Gwangju 61005, South Korea

^a e-mail: dongheekim@gist.ac.kr

Received: 13 August 2017
Received in final form: 15 October 2017
Published online: 11 December 2017

Abstract

We investigate the first-order transition in the spin-1 two-dimensional Blume-Capel model in square lattices by revisiting the transfer-matrix method. With large strip widths increased up to the size of 18 sites, we construct the detailed phase coexistence curve which shows excellent quantitative agreement with the recent advanced Monte Carlo results. In the deep first-order area, we observe the exponential system-size scaling of the spectral gap of the transfer matrix from which linearly increasing interfacial tension is deduced with decreasing temperature. We find that the first-order signature at low temperatures is strongly pronounced with much suppressed finite-size influence in the examined thermodynamic properties of entropy, non-zero spin population, and specific heat. It turns out that the jump at the transition becomes increasingly sharp as it goes deep into the first-order area, which is in contrast to the Wang–Landau results where finite-size smoothing gets more severe at lower temperatures.