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Correlation functions, free energies, and magnetizations in the two-dimensional random-field Ising model
S L de Queiroz1, R B Stinchcombe
1Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21945-970 Rio de Janeiro RJ, Brazil. sldq@if.ufrj.br
Summary
This study analyzes the 2D random-field Ising model near its critical temperature. We found that correlation length descriptions are limited, and magnetization distribution width scales with random-field intensity.
Area of Science:
- Statistical mechanics
- Condensed matter physics
- Ising model systems
Background:
- The two-dimensional random-field Ising model exhibits complex behavior near critical temperatures.
- Understanding spin-spin correlations and magnetization distributions is crucial for characterizing phase transitions.
Purpose of the Study:
- To investigate spin-spin correlation functions, free energies, and magnetizations in the 2D random-field Ising model.
- To analyze the validity of correlation length descriptions and the impact of random fields on magnetization distributions.
Main Methods:
- Utilizing transfer-matrix methods for calculations on long strips of varying widths (L=3-18).
- Analyzing probability distributions of correlation functions and magnetization.
- Applying finite-size scaling and crossover arguments.
Main Results:
- Effective correlation lengths are valid only for limited spin-spin distances.
- Fractional widths of correlation-function distributions saturate with system size (L^-2.2).
- The width of the uniform magnetization distribution scales as H0^(-3/7) with random-field intensity.
Conclusions:
- The study provides insights into the limitations of correlation length descriptions in disordered systems.
- It establishes a relationship between magnetization distribution and random-field strength.
- Findings contribute to the understanding of critical phenomena in disordered magnetic systems.