The interface tension in the improved Blume-Capel model

Abstract

We study interfaces with periodic boundary conditions in the low temperature phase of the improved Blume-Capel model on the simple cubic lattice. The interface free energy is defined by the difference of the free energy of a system with anti-periodic boundary conditions in one of the directions and that of a system with periodic boundary conditions in all directions. It is obtained by integration of differences of the corresponding internal energies over the inverse temperature. These differences can be computed efficiently by using a variance reduced estimator that is based on the exchange cluster algorithm. The interface tension is obtained from the interface free energy by using predictions based on effective interface models. By using our numerical results for the interface tension $\sigma$ and the correlation length $\xi$ obtained in previous work, we determine the universal amplitude ratios $R_{2nd,+}={\sigma }_0{f}_{2nd,+}^2=0.3863(6)$, $R_{2nd,-}={\sigma }_0{f}_{2nd,-}^2=0.1028(1)$ and $R_{exp,-}={\sigma }_0{f}_{exp,-}^2=0.1077(3)$. Our results are consistent with those obtained previously for the three-dimensional Ising model, confirming the universality hypothesis.

32 pages, 5 figures, discussion extended typos corrected

References in corpus (6)

• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• A Semidefinite Program Solver for the Conformal Bootstrap
• Thermodynamic Casimir Forces between a Sphere and a Plate: Monte Carlo Simulation of a Spin Model
• The interface free energy: Comparison of accurate Monte Carlo results for the 3D Ising model with effective interface models
• The partition function of interfaces from the Nambu-Goto effective string theory
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm