High-resolution mapping of the phase boundary of the honeycomb-lattice Blume--Capel ferromagnet
Abstract
We present a high-resolution numerical study of the spin-1 Blume-Capel ferromagnet on the honeycomb lattice (z=3). Using the Wang-Landau algorithm to estimate the joint density of states Ω(E1,E2) and field-mixing scaling, we map the first-order transition line and locate the tricritical point at (Δt,Tt)=[1.4820(2),0.4022(7)]. Independent Metropolis histogram reweighting for L=36 and $48$ yields a crossing temperature near $0.4039$, consistent with the Wang-Landau extrapolation. The field-mixing parameter is r=−1.585(19), while the coexistence-line slope gives r=−1.587(5). Normalizing by the zero-temperature field Δ0=zJ/2, the results for honeycomb, square, and triangular lattices give r/Δ0 between −1.057 and −1.067, about 6% larger in magnitude than the mean-field value. Simple-cubic estimates are compatible with this range but do not resolve dimensionality dependence. Finite-size scaling yields yt=1.795(7), consistent with the tricritical Ising value 9/5, while the fourth-order cumulant scaling agrees with yg=4/5. Deep in the first-order regime, the cumulant approaches the two-phase limit UQ→2/3. Multicanonical simulations up to L=64 yield an interface tension exponent μ=1.265(26), consistent with the tricritical prediction (d−1)/yg=5/4. We also map the continuous phase boundary, obtaining Tc(Δ=0)=1.157, and identify crossover effects from Ising to tricritical scaling near the tricritical point.
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BibTeX
@misc{filho2026highresolution,
title = {{High-resolution mapping of the phase boundary of the honeycomb-lattice Blume--Capel ferromagnet}},
author = {Eluiz C. M. Filho and Claudio J. DaSilva},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11068},
eprint = {2610.11068},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11068},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - High-resolution mapping of the phase boundary of the honeycomb-lattice Blume--Capel ferromagnet
AU - Eluiz C. M. Filho
AU - Claudio J. DaSilva
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.11068
UR - https://arxiv.org/abs/2610.11068
AB - We present a high-resolution numerical study of the spin-1 Blume-Capel ferromagnet on the honeycomb lattice (z=3). Using the Wang-Landau algorithm to estimate the joint density of states Ω(E_1,E_2) and field-mixing scaling, we map the first-order transition line and locate the tricritical point at (Δ_t,T_t)=[1.4820(2),0.4022(7)]. Independent Metropolis histogram reweighting for L=36 and $48$ yields a crossing temperature near $0.4039$, consistent with the Wang-Landau extrapolation. The field-mixing parameter is r=−1.585(19), while the coexistence-line slope gives r=−1.587(5). Normalizing by the zero-temperature field Δ_0=zJ/2, the results for honeycomb, square, and triangular lattices give r/Δ_0 between −1.057 and −1.067, about 6% larger in magnitude than the mean-field value. Simple-cubic estimates are compatible with this range but do not resolve dimensionality dependence. Finite-size scaling yields y_t=1.795(7), consistent with the tricritical Ising value 9/5, while the fourth-order cumulant scaling agrees with y_g=4/5. Deep in the first-order regime, the cumulant approaches the two-phase limit U_Q→2/3. Multicanonical simulations up to L=64 yield an interface tension exponent μ=1.265(26), consistent with the tricritical prediction (d−1)/y_g=5/4. We also map the continuous phase boundary, obtaining T_c(Δ=0)=1.157, and identify crossover effects from Ising to tricritical scaling near the tricritical point.
ER -