Abstract
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.
Highlights
The most important stage in describing phase transitions within the framework of the theory of critical phenomena is the description and determination of the critical point
We have demonstrated that a hysteresis effect occurs in the cease of the unstable state; in field theories, the tachyon can “survive”
Based on the fact that the mass of spontaneous symmetry breaking (SSB) soliton is analogous to odd power of the tachyon mass, we conclude that, in field theories, SSB solitons obtain a mass that becomes imaginary, as in the case with tachyons
Summary
The most important stage in describing phase transitions within the framework of the theory of critical phenomena is the description and determination of the critical point. The ground state (φ = 0, U ( φ) = 0) in the symmetric phase is the critical stable fixed point for r0 = 0 When this transition takes place, the position of the critical point does not change, but its character, namely its stability, changes. The only instability that occurs in SSB field theories is the appearance of the unstable critical point when m2 becomes negative. Through a numerical experiment with the 3D Ising model, one can follow the evolution of the SSB phenomenon, we found that the unstable state in which the tachyon “lives” can be significantly extended. The investigation into the existence of tachyonic fields and SSB solitons for extensive duration is the main purpose of this study
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