arXiv subjects

Dimitrios Mataragkas

Publications and source records attributed to Dimitrios Mataragkas.

3 recordsLinked to original sources

arXiv2026

Crossover and universality breaking in the dilute Baxter-Wu model

The critical behavior of the Baxter-Wu model belongs to the universality class of the four-state Potts model. While the introduction of annealed vacancies does not alter the criticality of the four-state Potts model, the dilute Baxter-Wu model has remained the subject of several competing scenarios. Here we investigate the phase diagram of the spin-$1$ Baxter-Wu model in the presence of a crystal field using transfer-matrix calculations and large-scale Monte Carlo simulations. Our results reveal a systematic evolution of the effective critical behavior with increasing crystal field, accompanied by increasingly strong finite-size corrections near the crossover to the first-order regime. Along the line of continuous transitions, the central charge remains close to $c=1$, while the scaling dimensions systematically deviate from the spin-$1/2$ limit as the crystal field increases, consistent with either continuously varying effective critical exponents or a slow crossover between competing critical behaviors. The first-order regime is independently characterized through multicanonical simulations, which confirm the expected finite-size scaling and interfacial behavior. Taken together, our results provide a unified picture of the dilute spin-$1$ Baxter-Wu model, substantially narrowing the range of possible scenarios for the crossover between continuous and first-order phase transitions.

cond-mat.stat-mech↗

arXiv2025

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

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.

cond-mat.stat-mech↗

arXiv2024

Tricriticality and finite-size scaling in the triangular Blume-Capel ferromagnet

We report on numerical simulations of the two-dimensional spin-$1$ Blume-Capel ferromagnet embedded in a triangular lattice. Utilizing a range of Monte Carlo and finite-size scaling techniques, we explore several critical aspects along the crystal field--temperature ($\Delta, T$) transition line. Wang-Landau simulations measuring the joint density of states in combination with the method of field mixing allow us to probe the phase coexistence curve in high resolution, determining the tricritical point $(\Delta_{\rm t}, T_{\rm t})$ with improved accuracy and verifying the tricritical exponents. Extensive multicanonical simulations identifying transition points across the phase diagram characterize the Ising universality class for $\Delta < \Delta_{\rm t}$ with precise determination of thermal and magnetic critical exponents expected in the second-order regime. On the other hand, for $\Delta > \Delta_{\rm t}$, a finite-size scaling analysis is dedicated to revealing the first-order signature in the surface tension that linearly increases upon lowering the temperature deeper into the first-order transition regime. Finally, a comprehensive picture of the phase diagram for the model is presented, collecting transition points obtained from the combined numerical approach in this study and previous estimates in the literature.

cond-mat.stat-mech↗