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Logarithmic corrections to correlation decay in two-dimensional random-bond Ising systems.

Jean C Lessa¹, S L A de Queiroz

¹Departamento de Física, Universidade Estadual de Feira de Santana, Campus Universitário, 44031-460 Feira de Santana BA, Brazil. jean@if.ufrj.br

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

|October 10, 2006

Summary

Researchers studied critical spin-spin correlations in disordered Ising systems using numerical methods. They found logarithmic corrections to decay, supporting conformal invariance predictions in strip geometries.

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Area of Science:

Condensed Matter Physics
Statistical Mechanics

Background:

Investigating critical phenomena in disordered systems is crucial for understanding complex materials.
Ising models with disorder exhibit rich statistical properties that are challenging to analyze.

Purpose of the Study:

To analyze the statistics of critical spin-spin correlation functions in disordered Ising systems.
To test for logarithmic corrections to power-law decay using conformal invariance on strip geometries.

Main Methods:

Numerical transfer-matrix techniques were employed to study the system.
Conformal invariance concepts were applied to analyze correlation functions.
Data fitting was performed using expressions specific to logarithmic corrections on strips.

Main Results:

Logarithmic corrections to pure power-law decay were observed with the correct sign for correlation function moments (n=0-4).
An interval of disorder strength was identified where corrections align with theoretical predictions.
A new fitting procedure showed good agreement with theoretical predictions in the low-disorder limit.

Conclusions:

The study confirms the presence of logarithmic corrections to correlation functions in disordered Ising systems on strips.
The findings support the applicability of conformal invariance in analyzing such systems.
The proposed fitting procedure offers a valuable tool for future investigations of disordered systems.