Disorder- driven gradual transition of the continuous symmetry- breaking phase transition / Z naključnim neredom spodbujen postopni fazni prehod sistema z zveznim faznim prehodom, ki zlomi simetrijo
Milan Svetec, Samo Kralj in Vlad Popa-Nita
Anali PAZU, 2 (2012), št. / No. 1, strani / pages 6-14
Celotno besedilo / Full text (PDF)
Abstract: We study the influence of random anisotropy type quenched disorder on the phase behavior of the system, which exhibits in undistorted case the 2nd order continuous symmetry breaking phase transition. Invoking the central limit theorem we express the free energy of the system in terms of the order parameter η and the characteristic length ξ of the gauge field ϕ. The latter exhibits the Goldstone fluctuation mode and is consequently extremely susceptible to the imposed disorder. In case of negligible distribution width ΔT of the local transition temperatures the disorder converts the 2nd order transition into a discontinuous one for W<WC, where Wrepresents the disorder strength. Above the critical disorder strength WC the transition becomes gradual. However for the finite width ΔT the transition becomes gradual for any W>0. We demonstrate that for large enough values of ΔT the system behavior is dominated by the distribution of temperatures, while the details of the random field interaction term play a secondary role. The influence of distribution of local (quasi) phase transitions is in most theoretical approaches dealing with randomly perturbed systems neglected from the outset.
Key words: quenched disorder; phase transition; symmetry breaking; gradual phase transition
Povzetek: Obravnavamo vpliv naključnega nereda na fazno obnašanje sistema, ki vsebuje v nemoteni fazi fazni prehod drugega reda. Z uporabo izreka o »centralni limiti« izrazimo prosto energijo sistema na podlagi ureditvenega parametra η in karakteristične dolžine ξ umeritvenega polja ϕ. Slednji se podreja Goldstone-ovimfluktuacijskim načinom in je izredno občutljiv na motnje. V primeru zanemarljive porazdelitve lokalnih temperatur faznega prehoda, nered pretvori fazni prehod drugega reda v nezvezni prehod za vrednosti W<WC, kjer je W jakost nereda. Nad kritično vrednostjo jakosti nereda WC postane prehod postopen. V primeru, ko imamo lokalno več različnih temperatur faznega prehoda – neko porazdelitev temperatur s širino ΔT, pa postane prehod postopen za vsako vrednost W>0. V članku pokažemo, da pri zadosti velikih vrednostih ΔT, fazno obnašanje določa porazdelitev temperatur, podrobnosti interakcij naključnega polja tukaj igrajo sekundarno vlogo.
Ključnebesede: naključni nered; fazni prehod; zlom simetrije; postopni prehod