Correlation-length-exponent relation for the two-dimensional random ising model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The two-dimensional (2D) Ising model is a fundamental model in statistical mechanics.
• Understanding the effects of quenched disorder (randomness) on critical phenomena is crucial.
• Investigating surface properties and correlation functions provides insights into bulk behavior.

Purpose of the Study:

• To determine the correlation length along a diagonal strip of the 2D random Ising model.
• To investigate the universality of critical behavior in the presence of bond dilution.
• To analyze the self-averaging and conformal covariance of the surface correlation function at the critical point.

Main Methods:

• Utilizing an iterative method based on the star-triangle transformation.
• Calculating the correlation length along the strip (xi(L)) for various strip widths (L<=21).
• Analyzing the ratio xi(L)/L at the bulk critical temperature.

Main Results:

• The ratio xi(L)/L approaches the universal value 2/pi for large strip widths.
• This universal ratio is independent of the dilution parameter (J1/J2).
• The surface correlation function demonstrates self-averaging and conformal covariance at the critical point, with a decay exponent eta(||)=1.

Conclusions:

• The 2D dilute Ising model exhibits universal critical behavior characterized by specific correlation length ratios.
• The employed iterative method provides high numerical precision for analyzing critical properties.
• The findings confirm theoretical predictions regarding self-averaging and conformal covariance in disordered systems.