Diversity of critical behavior within a universality class

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Critical Phenomena

Background:

• The O(n) symmetric phi^4 lattice model is a fundamental model for studying phase transitions.
• Spatial anisotropy can introduce complex behaviors not captured by isotropic models.
• Understanding critical phenomena in anisotropic systems is crucial for interpreting experimental data.

Purpose of the Study:

• To investigate the effects of spatial anisotropy on bulk and finite-size critical behavior.
• To analyze the absence of two-scale factor universality in anisotropic systems.
• To compare theoretical predictions with experimental and simulation data.

Main Methods:

• Renormalization-group theory within the minimal subtraction scheme at fixed dimension d (2
• Fixed-d finite-size approach preserving the exponential form of the order-parameter distribution function.
• Perturbation theory and comparison with Monte Carlo (MC) simulation data.

Main Results:

• Anisotropy parameters are observable via scattering experiments at the critical temperature (Tc).
• The fixed-d finite-size approach shows excellent agreement with 3D Ising model MC data.
• A minimum in the excess free energy scaling function is predicted, dependent on anisotropy.

Conclusions:

• Anisotropy significantly influences critical behavior, affecting free energy and Binder cumulant.
• The theory quantitatively matches MC simulations for the 2D Ising model's Binder cumulant dependence on NNN coupling.
• Nonuniversal anisotropy effects in the finite-size scaling regime exhibit restricted universality.