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Universal behavior of crossover scaling functions for continuous phase transitions
1Department of Physics of Complex Systems, Weizmann Institute of Science, 76100 Rehovot, Israel.
Physical Review Letters
|June 6, 2003
Summary
This study explores continuous phase transitions in two systems within the same universality class. Results confirm that the crossover function describing the transition is universal across different interaction ranges.
Area of Science:
- Statistical physics
- Condensed matter physics
Background:
- Continuous phase transitions into absorbing states are critical phenomena.
- Systems in the same universality class share critical exponents and scaling functions.
Purpose of the Study:
- To investigate the crossover behavior in systems transitioning to an absorbing state.
- To determine if the crossover function is universal across varying interaction ranges.
Main Methods:
- Studied two distinct models exhibiting continuous phase transitions.
- Analyzed the crossover from mean-field to non-mean-field scaling by varying interaction range.
- Applied a phenomenological scaling form to describe the crossover region.
Main Results:
- Both models belong to the same universality class.
- Observed a crossover from mean-field-like to non-mean-field scaling behavior.
- The phenomenological scaling form successfully described the full crossover region spanning several decades.
Conclusions:
- The crossover function governing the transition to an absorbing state is universal.
- This universality holds across different interaction ranges and system models.