Inverse Symmetry Breaking with 4d Lattice Simulations

We discuss the chiral symmetry restoration at high temperature and chemical potential for a four-fermion interaction theory in arbitrary dimensions ($2\leq D<4$). To investigate the ground state of the theory we calculate the effective potential and the gap equation using the method of the $1/N$ expansion. We study the phase structure at finite temperature and chemical potential and show critical curves which divide the symmetric and asymmetric phase. We find that the first a...

We discuss the phenomena of symmetry non-restoration and inverse symmetry breaking in the context of multi-scalar field theories at finite temperatures and present its consequences for the relativistic Higgs-Kibble multi-field sector as well as for a nonrelativistic model of hard core spheres. For relativistic scalar field models, it has been shown previously that temperature effects on the couplings do not alter, qualitatively, the phase transition pattern. Here, we show tha...

Using two different methods, we have determined the rescaling of the scalar condensate $Z\equiv Z_\phi$ near the critical line of a 4D Ising model. Our lattice data, in agreement with previous numerical indications, support the behavior $Z_\phi\sim \ln ({\Lambda})$, $\Lambda$ being the ultraviolet cutoff. This result is predicted in an alternative description of symmetry breaking where there are no upper bounds on the Higgs boson mass from `triviality'.

While it is possible to find examples of field theories with a spontaneously broken symmetry at high temperature, in renormalizable supersymmetric models any internal symmetry gets always restored. Recently, a counterexample was suggested in the context of nonrenormalizable supersymmetric theories. We show that non negligible higher loop effects actually restore the symmetry, without compromising the validity of perturbation theory. We give some arguments as to why the propos...

We have determined the rescaling of the scalar condensate $Z\equiv Z_\phi$ near the critical line of a 4D Ising model. Our lattice data, supporting previous numerical indications, confirm the behaviour $Z_\phi\sim \ln ({\rm cutoff})$. This result is predicted in an alternative description of symmetry breaking where there are no upper bounds on the Higgs boson mass from `triviality'.

Triviality of $\phi^4$ theory in four dimensions can be avoided if the bare coupling constant is negative in the UV. Theories with negative coupling can be put on the lattice if the integration domain for $\phi(x)$ is contour-deformed from the real to the complex domain. In 0+1d (quantum mechanics), one can recover results from $\mathcal{PT}$-symmetric quantum mechanics in this way. In this work, I report on an attempt to put negative coupling $\phi^4$ theory in 4 dimensions ...

Measurements of various physical quantities in the symmetry broken phase of the one component lattice $\phi^4_4$ with standard action, are shown to be consistent with the critical behavior obtained by renormalization group analyses. This is in contrast to recent conclusions by another group, who further claim that the unconventional scaling behavior they observe, when extended to the complete Higgs sector of the Standard Model, would alter the conventional triviality bound on...

We perform a detailed numerical investigation of the dynamics of broken symmetry $\lambda \phi^4$ field theory in 1+1 dimensions using a Schwinger-Dyson equation truncation scheme based on ignoring vertex corrections. In an earlier paper, we called this the bare vertex approximation (BVA). We assume the initial state is described by a Gaussian density matrix peaked around some non-zero value of $<\phi(0)>$, and characterized by a single particle Bose-Einstein distribution fun...

Considering marginally relevant and relevant deformations of the weakly coupled $(3+1)$-dimensional large $N$ conformal gauge theories introduced in arXiv:2011.13981, 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 f...

The difficulty is analysed in evaluating fluctuations in phase transition of finite-size system at temperature far below the critical point. Film system is discussed with one-component order parameter $\phi^4$ model for phase transition. Non-trivial vacuum state corresponding to minimum Hamiltonian is given approximately for various boundary conditions. It is shown that the spontaneous symmetry breaking plays an important role for such systems, and that perturbative calculati...