Criticality in the disordered N-color Ashkin-Teller model
Abstract
The N-color Ashkin-Teller model corresponds to N Ising models coupled by four-spin interactions. We consider the two-dimensional case in presence of quenched disorder and use scale invariant scattering theory to determine all the solutions of the exact renormalization group fixed points equations. The weak disorder sector is characterized by a solution that, for any fixed N larger than 1, is a line of fixed points with Ising thermal exponents and continuously varying magnetic exponents. The number of fixed point solutions allowed by the symmetries of the model increases at strong disorder illustrating the growing dependence on the distributions of the two random couplings. The presence of some critical exponents which do not depend on the symmetry parameter N confirms this type of superuniversality as a peculiar feature of random criticality.
Versions
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BibTeX
@misc{makoudi2026criticality,
title = {{Criticality in the disordered $N$-color Ashkin-Teller model}},
author = {Youssef Makoudi and Gesualdo Delfino},
howpublished = {arXiv},
year = {2026},
month = may,
doi = {10.48550/arxiv.2605.29810},
eprint = {2605.29810},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.29810},
}
RIS
TY - UNPB
TI - Criticality in the disordered N-color Ashkin-Teller model
AU - Youssef Makoudi
AU - Gesualdo Delfino
PY - 2026
DA - 2026/05/28
PB - arXiv
DO - 10.48550/arxiv.2605.29810
UR - https://arxiv.org/abs/2605.29810
AB - The N-color Ashkin-Teller model corresponds to N Ising models coupled by four-spin interactions. We consider the two-dimensional case in presence of quenched disorder and use scale invariant scattering theory to determine all the solutions of the exact renormalization group fixed points equations. The weak disorder sector is characterized by a solution that, for any fixed N larger than 1, is a line of fixed points with Ising thermal exponents and continuously varying magnetic exponents. The number of fixed point solutions allowed by the symmetries of the model increases at strong disorder illustrating the growing dependence on the distributions of the two random couplings. The presence of some critical exponents which do not depend on the symmetry parameter N confirms this type of superuniversality as a peculiar feature of random criticality.
ER -