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  • Open Access

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

Dimitrios Mataragkas, Alexandros Vasilopoulos, and Nikolaos G. Fytas*

Dong-Hee Kim†

  • School of Mathematics, Statistics and Actuarial Science, University of Essex, Colchester CO4 3SQ, United Kingdom

  • *Contact author: nikolaos.fytas@essex.ac.uk
  • †Contact author: dongheekim@gist.ac.kr
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Phys. Rev. Research 7, 033240 – Published 10 September, 2025

DOI: https://doi.org/10.1103/jfl3-f4kd

Abstract

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.

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Phys. Rev. Research 7, 033240– Published 10 September, 2025
  • Received 19 June 2025
  • Accepted 28 July 2025
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