Transfer-matrix approach to the Blume-Capel model on the triangular lattice

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Main Authors: Mataragkas, Dimitrios, Vasilopoulos, Alexandros, Fytas, Nikolaos G., Kim, Dong-Hee
Format: Preprint
Published: 2025
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author Mataragkas, Dimitrios
Vasilopoulos, Alexandros
Fytas, Nikolaos G.
Kim, Dong-Hee
author_facet Mataragkas, Dimitrios
Vasilopoulos, Alexandros
Fytas, Nikolaos G.
Kim, Dong-Hee
contents We investigate the spin-$1$ Blume-Capel model on an infinite strip of the triangular lattice using the transfer-matrix method combined with a sparse-matrix factorization technique. Through finite-size scaling analysis of numerically exact spectra for strip widths up to $L = 19$, we accurately locate the tricritical point improving upon recent Monte Carlo estimates. In the first-order regime, we observe exponential scaling of the spectral gap, reflecting the linear growth of interfacial tension as the temperature decreases below the tricritical point. Finally, we validate our tricritical point estimate through precise agreement with conformal field theory predictions for the tricritical Ising universality class. Our results underscore the continued utility of the transfer-matrix approach for studying phase transitions in complex lattice models.
format Preprint
id arxiv_https___arxiv_org_abs_2506_16483
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Transfer-matrix approach to the Blume-Capel model on the triangular lattice
Mataragkas, Dimitrios
Vasilopoulos, Alexandros
Fytas, Nikolaos G.
Kim, Dong-Hee
Statistical Mechanics
We investigate the spin-$1$ Blume-Capel model on an infinite strip of the triangular lattice using the transfer-matrix method combined with a sparse-matrix factorization technique. Through finite-size scaling analysis of numerically exact spectra for strip widths up to $L = 19$, we accurately locate the tricritical point improving upon recent Monte Carlo estimates. In the first-order regime, we observe exponential scaling of the spectral gap, reflecting the linear growth of interfacial tension as the temperature decreases below the tricritical point. Finally, we validate our tricritical point estimate through precise agreement with conformal field theory predictions for the tricritical Ising universality class. Our results underscore the continued utility of the transfer-matrix approach for studying phase transitions in complex lattice models.
title Transfer-matrix approach to the Blume-Capel model on the triangular lattice
topic Statistical Mechanics
url https://arxiv.org/abs/2506.16483