TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.4.122
TI  - Random matrices and the free energy of Ising-like models with disorder
PY  - 2024/10/30
UR  - https://scipost.org/SciPostPhys.17.4.122
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 4
SP  - 122
A1  - Gluth, Nils
AU  - Guhr, Thomas
AU  - Hucht, Alfred
AB  - We consider an Ising model with quenched surface disorder, the disorder average of the free energy is the main object of interest. Explicit expressions for the free energy distribution are difficult to obtain if the quenched surface spins take values of $± 1$. Thus, we choose a different approach and model the surface disorder by Gaussian random matrices. The distribution of the free energy is calculated. We chose skew-circulant random matrices and analytically compute the characteristic function of the free energy distribution. From the characteristic function we numerically calculate the distribution and show that it becomes log-normal for sufficiently large dimensions of the disorder matrices, and in the limit of infinitely large matrices tends to a Gaussian. Furthermore, we establish a connection to the central limit theorem.
ER  -

@Article{10.21468/SciPostPhys.17.4.122,
	title={{Random matrices and the free energy of Ising-like models with disorder}},
	author={Nils Gluth and Thomas Guhr and Alfred Hucht},
	journal={SciPost Phys.},
	volume={17},
	pages={122},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.4.122},
	url={https://scipost.org/10.21468/SciPostPhys.17.4.122},
}