Crossover between a displacive and an order-disorder phase transition

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Computational Physics

Background:

• The discrete phi(4) model describes phase transitions in systems with anharmonic oscillators.
• Understanding the transition from displacive to order-disorder behavior is crucial for various physical systems.
• A single dimensionless parameter 'a' governs the system's behavior, allowing continuous tuning between limits.

Purpose of the Study:

• To investigate the phase transition in a 3D discrete phi(4) model.
• To calculate the transition temperature T(c) and order parameter temperature dependence for a wide range of the parameter 'a'.
• To compare simulation and analytical results with existing approximations and introduce a novel approximation scheme.

Main Methods:

• Monte Carlo (MC) simulations were employed to study the system.
• Analytical methods, including mean-field and independent-mode approximations, were used.
• A new approximation scheme involving an auxiliary system was developed.

Main Results:

• MC calculations for T(c) showed excellent agreement with known asymptotic values for small and large 'a'.
• The study successfully calculated the order parameter's temperature dependence down to T=0 for diverse 'a' values.
• The developed approximation scheme predicted T(c) within 5% error and described the order parameter's behavior well.

Conclusions:

• The study provides a comprehensive analysis of the phase transition in the 3D discrete phi(4) model.
• The developed approximation scheme offers a reliable and accurate method for predicting system behavior.
• Results validate MC simulations and offer insights into tuning system properties via the parameter 'a'.