Phase Transitions in Disordered Systems: The Example of the Random-Field Ising Model in Four Dimensions.
By performing a high-statistics simulation of the D=4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.
Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom.
Nikolaos G
NG
Fytas
Departamento de Física Téorica I, Universidad Complutense, 28040 Madrid, Spain.|Instituto de Biocomputacíon y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain.
Víctor
V
Martín-Mayor
LPTHE (Unité mixte de recherche du CNRS UMR 7589), Université Pierre et Marie Curie-Paris 6, 4 place Jussieu, 75252 Paris Cedex 05, France.
Marco
M
Picco
Laboratoire de Physique Théorique de l'Ecole Normale Supérieure (Unité Mixte de Recherche du CNRS et de l'Ecole Normale Supérieure, associée à l'Université Pierre et Marie Curie, PARIS VI) 24 rue Lhomond, 75231 Paris Cedex 05, France.
Nicolas
N
Sourlas