Gibbsianness versus non-Gibbsianness of time-evolved planar rotor models

A.C.D. van Enter and W.M. Ruszel

Stochastic Processes and their Applications, 2009, vol. 119, issue 6, 1866-1888

Abstract: We study the Gibbsian character of time-evolved planar rotor systems (that is, systems which have two-component, classical XY, spins) on , d>=2, in the transient regime, evolving with stochastic dynamics and starting from an initial Gibbs measure [nu]. We model the system with interacting Brownian diffusions moving on circles. We prove that for small times t and arbitrary initial Gibbs measures [nu], or for long times and both high- or infinite-temperature initial measure and dynamics, the evolved measure [nu]t stays Gibbsian. Furthermore, we show that for a low-temperature initial measure [nu] evolving under infinite-temperature dynamics there is a time interval (t0,t1) such that [nu]t fails to be Gibbsian for d>=2.

Keywords: Gibbs; property; Non-Gibbsianness; Stochastic; dynamics; XY-spins (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(08)00143-9
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:119:y:2009:i:6:p:1866-1888

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().