Spontaneous symmetry breaking in the effective potential

Patterns of symmetry breaking induced by potentials at the boundary of free O(N)O(N)-models in d=3- \epsilond=3−ϵ dimensions are studied. We show that the spontaneous symmetry breaking in these theories leads to a boundary RG flow ending with N - 1N−1 Neumann modes in the IR. The possibility of fluctuation-induced symmetry breaking is examined and we derive a general formula for computing one-loop effective potentials at the boundary. Using the \epsilonϵ-expansion we test these ideas in an O(N)\oplus O(N)O(N)⊕O(N)-model with boundary interactions. We determine the RG flow diagram of this theory and find that it has an IR-stable critical point satisfying conformal boundary conditions. The leading correction to the effective potential is computed and we argue the existence of a phase boundary separating the region flowing to the symmetric fixed point from the region flowing to a symmetry-broken phase with a combination of Neumann and Dirchlet boundary conditions.

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Spontaneous Symmetry Breaking and Its Pattern of Scales

Symmetry ◽

10.3390/sym12122037 ◽

2020 ◽

Vol 12 (12) ◽

pp. 2037

Author(s):

Maurizio Consoli ◽

Leonardo Cosmai

Keyword(s):

Phase Transition ◽

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Order Phase Transition ◽

Effective Potential ◽

Top Quark ◽

Vector Boson ◽

Atlas Collaboration ◽

Point Energy ◽

Scalar Sector

Spontaneous Symmetry Breaking (SSB) in λΦ4 theories is usually described as a 2nd-order phase transition. However, most recent lattice calculations indicate instead a weakly 1st-order phase transition as in the one-loop and Gaussian approximations to the effective potential. This modest change has non-trivial implications. In fact, in these schemes, the effective potential at the minima has two distinct mass scales: (i) a first mass mh associated with its quadratic curvature and (ii) a second mass Mh associated with the zero-point energy which determines its depth. The two masses describe different momentum regions in the scalar propagator and turn out to be related by Mh2∼mh2ln(Λs/Mh), where Λs is the ultraviolet cutoff of the scalar sector. Our lattice simulations of the propagator are consistent with this two-mass picture and, in the Standard Model, point to a value Mh∼700 GeV. However, despite its rather large mass, this heavier excitation would interact with longitudinal W’s and Z’s with the same typical coupling of the lower-mass state and would therefore represent a rather narrow resonance. Two main novel implications are emphasized in this paper: (1) since vacuum stability depends on the much larger Mh, and not on mh, SSB could originate within the pure scalar sector regardless of the other parameters of the theory (e.g., the vector-boson and top-quark mass) (2) if the smaller mass were fixed at the value mh=125 GeV measured at LHC, the hypothetical heavier state Mh would then naturally fit with the peak in the 4-lepton final state observed by the ATLAS Collaboration at 700 GeV.

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Spontaneous symmetry breaking of dislocation core in SrTiO3

Materials Today Physics ◽

10.1016/j.mtphys.2021.100453 ◽

2021 ◽

pp. 100453

Author(s):

Hetian Chen ◽

Di Yi ◽

Ben Xu ◽

Jing Ma ◽

Cewen Nan

Keyword(s):

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Dislocation Core

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Tachyons and Solitons in Spontaneous Symmetry Breaking in the Frame of Field Theory

Symmetry ◽

10.3390/sym13081358 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1358

Author(s):

Yiannis Contoyiannis ◽

Michael P. Hanias ◽

Pericles Papadopoulos ◽

Stavros G. Stavrinides ◽

Myron Kampitakis ◽

...

Keyword(s):

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Critical Point ◽

Universality Class ◽

Lattice Simulation ◽

Ginzburg Landau ◽

Spin Lattice ◽

Nuclear Collisions ◽

Ising Spin ◽

Relativistic Nuclear Collisions

This paper presents our study of the presence of the unstable critical point in spontaneous symmetry breaking (SSB) in the framework of Ginzburg–Landau (G-L) free energy. Through a 3D Ising spin lattice simulation, we found a zone of hysteresis where the unstable critical point continued to exist, despite the system having entered the broken symmetry phase. Within the hysteresis zone, the presence of the kink–antikink SSB solitons expands and, therefore, these can be observed. In scalar field theories, such as Higgs fields, the mass of this soliton inside the hysteresis zone could behave as a tachyon mass, namely as an imaginary quantity. Due to the fact that groups Ζ(2) and SU(2) belong to the same universality class, one expects that, in future experiments of ultra-relativistic nuclear collisions, in addition to the expected bosons condensations, structures of tachyon fields could appear.

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