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Universal critical behavior of aperiodic ferromagnetic models
1Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP, Brazil.
Summary
Geometric fluctuations in ferromagnetic Potts models alter critical behavior. Relevant fluctuations lead to novel critical behavior and distinct critical exponents, differing from uniform cases.
Area of Science:
- Statistical physics
- Condensed matter physics
Background:
- Ferromagnetic Potts models are crucial for understanding magnetism.
- Geometric fluctuations and aperiodic interactions significantly impact material properties.
Purpose of the Study:
- Investigate how geometric fluctuations affect critical behavior in q-state ferromagnetic Potts models.
- Analyze the influence of aperiodic exchange interactions on generalized diamond hierarchical lattices.
Main Methods:
- Utilized exact recursion relations in parameter space to analyze critical behavior.
- Employed scaling arguments to calculate the specific heat critical exponent (alpha).
- Performed direct numerical analysis of thermodynamic free energy singularities to validate predictions.
Main Results:
- Identified a nontrivial diagonal fixed point governing universal critical behavior for irrelevant fluctuations.
- Observed the emergence of a two-cycle and novel critical behavior for relevant fluctuations.
- Calculated critical exponents, finding they are independent of exchange interaction strengths.
Conclusions:
- Geometric fluctuations introduce novel critical behaviors in ferromagnetic Potts models.
- The critical exponent alpha for specific heat differs from uniform cases.
- Scaling predictions show excellent agreement with numerical analysis, especially for larger q values.
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