Global persistence exponent of the two-dimensional Blume-Capel model

Area of Science:

• Statistical physics
• Condensed matter physics
• Non-equilibrium systems

Background:

• The Blume-Capel model is a fundamental model in statistical physics, used to study phase transitions.
• Understanding non-equilibrium critical dynamics is crucial for describing systems far from thermodynamic equilibrium.
• Quenching a system to its critical point can reveal universal behaviors.

Purpose of the Study:

• To calculate the global persistence exponent theta(g) for the 2D Blume-Capel model.
• To investigate the non-equilibrium critical dynamics after quenching to the critical point.
• To determine if universality classes differ at the critical line and tricritical point.

Main Methods:

• Numerical simulations of the two-dimensional Blume-Capel model.
• Quenching the system to the critical point from various initial states (disordered and low magnetization).
• Analysis of the global persistence exponent theta(g) to characterize critical dynamics.

Main Results:

• The global persistence exponent theta(g) was estimated for the 2D Blume-Capel model.
• Ising-like universality was observed along the critical line.
• A different value for the global persistence exponent, theta(g)=1.080(4), was found at the tricritical point.

Conclusions:

• The non-equilibrium critical dynamics of the 2D Blume-Capel model exhibit distinct behaviors at the critical line and tricritical point.
• The findings suggest that universality classes can differ in non-equilibrium phase transitions.
• This study provides valuable insights into the complex dynamics of quenched systems.