Scaling functions for systems with finite range of interaction

Area of Science:

• Statistical Physics
• Computational Physics

Background:

• Nonequilibrium systems exhibit complex behaviors not fully described by equilibrium statistical mechanics.
• Understanding universality and critical phenomena in these systems is crucial for theoretical advancements.

Purpose of the Study:

• To numerically determine scaling functions for magnetization, susceptibility, and Binder's cumulant in two nonequilibrium models.
• To investigate the universality of these functions across varying interaction ranges.
• To accurately estimate long-range exponents governing critical amplitude decay.

Main Methods:

• Monte Carlo simulations were employed on square lattices for the block voter model (BVM).
• Monte Carlo simulations were performed on random graphs for the majority-vote model (MVM).
• Data collapse analysis was used to verify universality across multiple system sizes and interaction ranges.

Main Results:

• Satisfactory data collapse was achieved for both models, supporting the universality hypothesis.
• Accurate estimations of long-range exponents were obtained.
• Static exponents were found to be consistent with Ising-like behavior for BVM and classical for MVM.

Conclusions:

• The scaling functions of the studied nonequilibrium models are universal.
• The long-range exponents and static exponents provide insights into the critical behavior of these systems.
• The findings contribute to the understanding of critical phenomena in interacting particle systems.