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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Cluster-size heterogeneity in the two-dimensional Ising model.

Woo Seong Jo¹, Su Do Yi, Seung Ki Baek

¹BK21 Physics Research Division and Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 4, 2012

Summary

This summary is machine-generated.

This study numerically examines cluster size heterogeneity in the 2D Ising model, confirming a proposed scaling form. Results align with theoretical fractal and Fisher exponents, highlighting significant finite-size effects.

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Area of Science:

Statistical physics
Complex systems

Background:

The two-dimensional Ising model is a fundamental model in statistical physics.
Understanding cluster size distribution is crucial for characterizing phase transitions and critical phenomena.
Percolation theory provides a framework for studying the geometry of clusters.

Purpose of the Study:

To numerically investigate the heterogeneity in cluster sizes within the two-dimensional Ising model.
To verify the recently proposed scaling form for cluster-size heterogeneity in the context of percolation problems.
To determine the scaling exponents related to cluster size distribution and compare them with theoretical predictions.

Main Methods:

Numerical simulations of the two-dimensional Ising model.
Finite-size scaling analysis to extract critical exponents.
Comparison of numerical results with theoretical values for fractal dimension and Fisher exponent.

Main Results:

The numerical investigation confirms the proposed scaling form for cluster size heterogeneity.
The obtained scaling exponents are consistent with the theoretical fractal dimension (d(f)) and Fisher exponent (τ).
Strong finite-size effects were identified, attributed to the geometric nature of cluster-size heterogeneity.

Conclusions:

The study validates the scaling theory for cluster size heterogeneity in the 2D Ising model.
Numerical evidence supports the theoretical values of critical exponents governing cluster distributions.
The findings underscore the importance of considering finite-size effects in analyzing geometric properties of critical systems.