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Exact Solution of the Glauber-Ising Model on the Finite-Length Semi-Open Chain
Malte Henkel1,2
1Laboratoire de Physique et Chimie Théoriques (CNRS UMR 7019), Université de Lorraine Nancy, P.O. Box 70239, F-54506 Vandœuvre-lès-Nancy, France.
Entropy (Basel, Switzerland)
|July 28, 2026
Summary
We derived the exact time-space correlation function for the 1D Glauber-Ising model at zero temperature. This allows us to determine probabilities for a related coagulation-diffusion process and confirm scaling theory predictions.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Mathematical Physics
Background:
- The Glauber-Ising model is a fundamental model in statistical mechanics.
- Understanding dynamics on finite lattices is crucial for theoretical and experimental physics.
- Finite-size scaling theory provides a framework for analyzing system behavior near critical points.
Purpose of the Study:
- To obtain the exact time-space correlation function for the 1D Glauber-Ising model under specific conditions.
- To investigate the dual 1D coagulation-diffusion process.
- To validate dynamical finite-size scaling theory predictions.
Main Methods:
- Exact solution of the 1D Glauber-Ising model.
- Quenching the system to zero temperature (T=0).
- Analysis on a semi-open lattice of finite size N.
Main Results:
- The exact time-space correlation function was derived.
- The empty-interval probability for the dual 1D coagulation-diffusion process was deduced.
- The long-time decay of particle concentration was reproduced.
Conclusions:
- The obtained results align with dynamical finite-size scaling theory.
- The study provides exact analytical results for a fundamental statistical model.
- This work offers insights into the behavior of related stochastic processes.
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