Transfer-matrix approach to the Blume-Capel model on the triangular lattice
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911146787733504 |
|---|---|
| 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 |