Revisiting transfer-matrix calculations in the two-dimensional Blume-Capel model

Abstract

We study the phase transitions in the two-dimensional Blume-Capel model by using the transfer matrix method. The sparse-matrix decomposition technique and modernized Krylov subspace method allows us to access up to 18x18 lattices, providing clear advantages in finite-size-scaling analysis over those performed with small lattices in the previous transfer-matrix-based works [1,2]. By revisiting the phase diagram in the area of high crystal anisotropy, we provide the first-order transition line in improved accuracy and numerically confirm the Ising tricritical exponents through finite-size-scaling tests on correlation and persistence lengths. [1] P. D. Beal, Phys. Rev. B 33, 1717 (1986). [2] J. C. Xavier, F. C. Alcaraz, D. Pena Lara, and J. A. Plascak, Phys. Rev. B 57, 11575 (1998).