Phase Transitions and Continuous Symmetry Breaking

Abstract Considering marginally relevant and relevant deformations of the weakly coupled (3 + 1)-dimensional large N conformal gauge theories introduced in [1], we study the patterns of phase transitions in these systems that lead to a symmetry-broken phase in the high temperature limit. These deformations involve only the scalar fields in the models. The marginally relevant deformations are obtained by varying certain double trace quartic couplings between the scalar fields. The relevant deformations, on the other hand, are obtained by adding masses to the scalar fields while keeping all the couplings frozen at their fixed point values. At the N → ∞ limit, the RG flows triggered by these deformations approach the aforementioned weakly coupled CFTs in the UV regime. These UV fixed points lie on a conformal manifold with the shape of a circle in the space of couplings. As shown in [1], in certain parameter regimes a subset of points on this manifold exhibits thermal order characterized by the spontaneous breaking of a global ℤ2 or U(1) symmetry and Higgsing of a subset of gauge bosons at all nonzero temperatures. We show that the RG flows triggered by the marginally relevant deformations lead to a weakly coupled IR fixed point which lacks the thermal order. Thus, the systems defined by these RG flows undergo a transition from a disordered phase at low temperatures to an ordered phase at high temperatures. This provides examples of both inverse symmetry breaking and symmetry nonrestoration. For the relevant deformations, we demonstrate that a variety of phase transitions are possible depending on the signs and magnitudes of the squares of the masses added to the scalar fields. Using thermal perturbation theory, we derive the approximate values of the critical temperatures for all these phase transitions. All the results are obtained at the N → ∞ limit. Most of them are found in a reliable weak coupling regime and for others we present qualitative arguments.

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Symmetry breaking and phase transitions in general statistics

Physical Review D ◽

10.1103/physrevd.28.1358 ◽

1983 ◽

Vol 28 (6) ◽

pp. 1358-1363

Author(s):

R. Y. Levine ◽

Y. Tomozawa

Keyword(s):

Phase Transitions ◽

Symmetry Breaking

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Role of the electromagnetic field in the formation of domains in the process of symmetry-breaking phase transitions

Physical Review A ◽

10.1103/physreva.74.022105 ◽

2006 ◽

Vol 74 (2) ◽

Cited By ~ 46

Author(s):

Emilio Del Guidice ◽

Giuseppe Vitiello

Keyword(s):

Electromagnetic Field ◽

Phase Transitions ◽

Symmetry Breaking

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300 nm bandwidth adiabatic SOI polarization splitter-rotators exploiting continuous symmetry breaking

Optics Express ◽

10.1364/oe.23.019261 ◽

2015 ◽

Vol 23 (15) ◽

pp. 19261 ◽

Cited By ~ 14

Author(s):

Luciano Socci ◽

Vito Sorianello ◽

Marco Romagnoli

Keyword(s):

Symmetry Breaking ◽

Polarization Splitter ◽

Continuous Symmetry

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Dark matter reflection of particle symmetry

Modern Physics Letters A ◽

10.1142/s0217732317400016 ◽

2017 ◽

Vol 32 (15) ◽

pp. 1740001 ◽

Cited By ~ 3

Author(s):

Maxim Yu. Khlopov

Keyword(s):

Dark Matter ◽

Phase Transitions ◽

Symmetry Breaking ◽

Early Universe ◽

Topological Defects ◽

Elementary Particles ◽

Nonlinear Structures ◽

The Relationship ◽

New Particles

In the context of the relationship between physics of cosmological dark matter and symmetry of elementary particles, a wide list of dark matter candidates is possible. New symmetries provide stability of different new particles and their combination can lead to a multicomponent dark matter. The pattern of symmetry breaking involves phase transitions in the very early Universe, extending the list of candidates by topological defects and even primordial nonlinear structures.

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