scholarly journals XYmodels with disorder and symmetry-breaking fields in two dimensions

1998 ◽  
Vol 58 (13) ◽  
pp. 8667-8682 ◽  
Author(s):  
Stefan Scheidl ◽  
Michael Lehnen
Keyword(s):  
Symmetry Breaking ◽  
Two Dimensions

scholarly journals Holographic Ward identities for symmetry breaking in two dimensions

2017 ◽  
Vol 2017 (4) ◽  
Author(s):  
Riccardo Argurio ◽  
Gaston Giribet ◽  
Andrea Marzolla ◽  
Daniel Naegels ◽  
J. Anibal Sierra-Garcia
Keyword(s):  
Symmetry Breaking ◽  
Two Dimensions ◽  
Ward Identities

THE NATURE OF SYMMETRY BREAKING IN THE SUPERFLUID PHASE TRANSITION IN TWO DIMENSIONS

1994 ◽  
Vol 08 (06) ◽  
pp. 381-392
Author(s):  
ACHILLES D. SPELIOTOPOULOS ◽  
HARRY L. MORRISON
Keyword(s):  
Phase Transition ◽  
Gauge Symmetry ◽  
Symmetry Breaking ◽  
Bose Gas ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Superfluid Phase ◽  
Ensemble Theory ◽  
Ideal Bose Gas

The nature of symmetry breaking in the superfluid phase transition in two dimensions is studied. It is shown that, like superfluidity in three dimensions, the superfluid phase transition in two dimensions is characterized by the breaking of a U(1) gauge symmetry. The phase transition does not so much resemble the superfluid phase transition in three dimensions, however, as it does Bogolubov’s η-ensemble theory of the condensation of an ideal Bose gas.

The arithmetic symmetry of colored crystals: classification of 2-color 2-lattices

2004 ◽  
Vol 37 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Giuseppe Fadda ◽  
Giovanni Zanzotto
Keyword(s):  
Symmetry Breaking ◽  
Crystal Structures ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Systematic Classification ◽  
Black And White ◽  
Detailed Classification

A framework for the detailed classification of general crystal structures, based on an arithmetic criterion, has been proposed in recent years. In this paper it is shown how this method can also be applied to enumerate colored crystals. To illustrate this approach, the systematic classification in the simplest case,i.e.of `2-color 2-lattices', in two and three dimensions (two- and three-dimensional crystals with two differently colored atoms per unit translational cell) is presented. 51 distinct types of 2-color 2-lattices are found in three dimensions (ten types in two dimensions); this gives a complete catalog of the simplest crystal structures that are theoretically possible for two-element compounds. Among the 51 2-lattices, all those which already have aStrukturberichtedenomination are retrieved, as well as the 22 `black-and-white lattices' considered in the theory of magnetic crystals. The symmetry hierarchies and symmetry-breaking possibilities for 2-color 2-lattices are also determined in two and three dimensions.

Gross–Neveu–Yukawa and Gross–Neveu models

2021 ◽  
pp. 489-506
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Phase Transition ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Particle Physics ◽  
Continuous Phase ◽  
Two Dimensions ◽  
Fermion Mass ◽  
Dirac Fermions ◽  
Mass Generation ◽  
Four Dimensions

In this chapter, a model is considered that can be defined in continuous dimensions, the Gross– Neveu–Yukawa (GNY) model, which involves N Dirac fermions and one scalar field. The model has a continuous U(N) symmetry, and a discrete symmetry, which prevents the addition of a fermion mass term to the action. For a specific value of a coefficient of the action, the model undergoes a continuous phase transition. The broken phase illustrates a mechanism of spontaneous symmetry breaking, leading to spontaneous fermion mass generation like in the Standard Model (SM) of particle physics. In four dimensions, the GNY can be considered as a toy model to represent the interactions between the top quark and the Higgs boson, the heaviest particles of the SM of fundamental interactions, when the gauge fields are omitted. The model is renormalizable in four dimensions and its renormalization group (RG) properties can be studied in d = 4 and d = 4 − ϵ dimensions. A model of self-interacting fermions with the same symmetries and fermion content, the Gross–Neveu (GN) model, has been widely studied. In perturbation theory, for d > 2, it describes only a phase with massless fermions but, in d = 2 + ϵ dimensions, the RG indicates that, at a critical value of the coupling constant, the model experiences a phase transition. In two dimensions, it is renormalizable and exhibits the phenomenon of asymptotic freedom. The massless phase becomes infrared unstable and there is strong evidence that the spectrum corresponds to spontaneous symmetry breaking and fermion mass generation.

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