A Monte Carlo study of surface critical phenomena: The special point

Abstract

We study the special point in the phase diagram of a semi-infinite system, where the bulk transition is in the three-dimensional Ising universality class. To this end we perform a finite size scaling study of the improved Blume-Capel model on the simple cubic lattice with two different types of surface interactions. In order to check for the effect of leading bulk corrections we have also simulated the spin-1/2 Ising model on the simple cubic lattice. We have accurately estimated the surface enhancement coupling at the special point of these models. We find $y_{t_s}=0.718(2)$ and $y_{h_s}=1.6465(6)$ for the surface renormalization group exponents of the special transitions. These results are compared with previous ones obtained by using field theoretic methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore we study the behaviour of the surface transition near the special point and finally we discuss films with special boundary conditions at one surface and fixed ones at the other.

21 pages, 2 figures. figure 1 replaced, various typos corrected

References in corpus (2)

• The critical exponents of the superfluid transition in He4
• The thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class

Cited by in corpus (21)

• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Boundary critical behavior of the three-dimensional Heisenberg universality class
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• The dynamic critical exponent $z$ of the three-dimensional Ising universality class: Monte Carlo simulations of the improved Blume-Capel model
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Surface criticality of antiferromagnetic Potts model
• Monte Carlo simulations of dynamic phase transitions in ultrathin Blume-Capel films
• Critical Casimir effect in films for generic non-symmetry-breaking boundary conditions
• Conformal symmetry of the critical 3D Ising model inside a sphere
• Surface critical properties of the three-dimensional clock model
• A structural test for the conformal invariance of the critical 3d Ising model
• Critical Casimir forces in the presence of random surface fields
• Monte Carlo simulations of dynamic phase transitions in ferromagnetic thin-films
• Why boundary conditions do not generally determine the universality class for boundary critical behavior
• Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge
• The ordinary surface universality class of the three-dimensional O($N$) model
• Collective non-equilibrium dynamics at surfaces and the spatio-temporal edge
• Fluctuation induced forces in critical films with disorder at their surfaces
• Boundary operator product expansion coefficients of the three-dimensional Ising universality class
• Critical relaxation and the combined effects of spatial and temporal boundaries