Global persistence exponent in critical dynamics: finite-size-induced crossover

Area of Science:

• Statistical physics
• Condensed matter physics
• Phase transitions

Background:

• Global order parameters are crucial for understanding critical phenomena.
• Confinement effects in physical systems can alter critical behavior.
• Persistence properties probe the dynamics of order parameter decay.

Purpose of the Study:

• To extend the definition of a global order parameter to confined critical systems.
• To investigate the persistence of this order parameter after a quench to the critical point.
• To characterize the crossover behavior and its dependence on system geometry.

Main Methods:

• Theoretical analysis of a critical system confined between two parallel plates of separation L.
• Study of the global order parameter's persistence probability.
• Identification of crossover behavior and associated exponents.

Main Results:

• A generalized definition for global order parameters in confined systems was established.
• The persistence property of the order parameter exhibits a crossover.
• A nonuniversal exponent characterizes this crossover, dependent on the L/ξ ratio (system size to dynamic length scale).

Conclusions:

• Confinement significantly influences the critical dynamics of order parameters.
• The observed crossover highlights a transition in behavior as system size varies relative to the dynamic length scale.
• The findings provide insights into the statistical mechanics of finite-sized critical systems.