Journal ArticleDOI
Random-Field Instability of the Ordered State of Continuous Symmetry
Yoseph Imry,Shang-keng Ma +1 more
TLDR
In this article, it was shown that when the order parameter has a continuous symmetry, the ordered state is unstable against an arbitrarily weak random field in less than four dimensions and the borderline dimensionality above which mean-field-theory results hold is six.Abstract:
Phase transitions are considered in systems where the field conjugate to the order parameter is static and random. It is demonstrated that when the order parameter has a continuous symmetry, the ordered state is unstable against an arbitrarily weak random field in less than four dimensions. The borderline dimensionality above which mean-field-theory results hold is six. (auth)read more
Citations
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Journal ArticleDOI
The Ising antiferromagnet in a uniform field
TL;DR: In this article, the antiferromagnetic Ising model in a uniform field on a square lattice is studied by a position-space renormalization group approach, where a self-dual cluster that preserves sublattice symmetry is employed: at each site of the cluster, the coupling to the field is chosen to be proportional to the coordination number of that site.
Journal ArticleDOI
Sharp-interface limit of a ginzburg-landau functional with a random external field
Nicolas Dirr,Enza Orlandi +1 more
TL;DR: This work adds a random bulk term, modeling the interaction with the impurities of the medium, to a standard functional in the gradient theory of phase transitions consisting of a gradient term with a double-well potential, and derives the macroscopic cost of low energy “excited” states.
Dissertation
Influence du champ aléatoire et des interactions à longue portée sur le comportement critique du modèle d'Ising : une approche par le groupe de renormalisation non perturbatif
TL;DR: In this article, the authors consider a generalisation of the modele d’Ising in the presence of a champ magnetique aleatoire and show that it is possible to construct a model with dimensions in the dimension d = 1, 2, 3, 4 and 5.
Applications of Spin Glasses across Disciplines: From Complex Systems to Quantum Computing and Algorithm Development
TL;DR: In this paper, the authors studied the equilibrium and non-equilibrium properties of Boolean decision problems with competing interactions on scale-free networks in an external bias (a magnetic field).
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