{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T17:38:00Z","timestamp":1775410680103,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,7,27]],"date-time":"2021-07-27T00:00:00Z","timestamp":1627344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents our study of the presence of the unstable critical point in spontaneous symmetry breaking (SSB) in the framework of Ginzburg\u2013Landau (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\u2013antikink 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 \u0396(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.<\/jats:p>","DOI":"10.3390\/sym13081358","type":"journal-article","created":{"date-parts":[[2021,7,27]],"date-time":"2021-07-27T03:53:53Z","timestamp":1627358033000},"page":"1358","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Tachyons and Solitons in Spontaneous Symmetry Breaking in the Frame of Field Theory"],"prefix":"10.3390","volume":"13","author":[{"given":"Yiannis","family":"Contoyiannis","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronics Engineering, University of West Attica, 12244 Athens, Greece"},{"name":"Department of Physics, University of Athens, 15784 Athens, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0918-9343","authenticated-orcid":false,"given":"Michael P.","family":"Hanias","sequence":"additional","affiliation":[{"name":"Department of Physics, International Hellenic University, 65404 Kavala, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8268-253X","authenticated-orcid":false,"given":"Pericles","family":"Papadopoulos","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, University of West Attica, 12244 Athens, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8484-1402","authenticated-orcid":false,"given":"Stavros G.","family":"Stavrinides","sequence":"additional","affiliation":[{"name":"School of Science and Technology, International Hellenic University, 57001 Thessaloniki, Greece"}]},{"given":"Myron","family":"Kampitakis","sequence":"additional","affiliation":[{"name":"Hellenic Electricity Distribution Network Operator SA, Network Major Installations Department, 72 Athinon Ave., 18547 N.Faliro, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5928-4587","authenticated-orcid":false,"given":"Stelios M.","family":"Potirakis","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, University of West Attica, 12244 Athens, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7342-0557","authenticated-orcid":false,"given":"Georgios","family":"Balasis","sequence":"additional","affiliation":[{"name":"Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Metaxa and Vasileos Pavlou, Penteli, 15236 Athens, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,27]]},"reference":[{"key":"ref_1","unstructured":"Huang, K. 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