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Surface tension in the Ising model
| Content Provider | Semantic Scholar |
|---|---|
| Author | Abraham, David Gallavotti, Giovanni Martin-Löf, Anders |
| Copyright Year | 1972 |
| Abstract | In this note we consider a 2–dimensional Ising ferromagnet with nearest neighbor coupling J = − 1 2 . We suppose the system enclosed in a box Ω periodicized in one direction (i.e. Ω is regard as a cylinder). |Ω| denotes its area. Suppose that β = 1/kT is large enough so that a spontaneous magnetization m is possible in zero external field. Let us ask how it is possible to describe, from a microscopic point of view, the phenomenon of coexistence of two oppositely magnetized phases and how one can give a purely microscopic definition of surface tension (). Minlos and Sinai have first developed a powerful technique to deal with this type of questions (). In this paper we describe the results we obtained on the surface tension problem by using their methods nd ides we shall systematically skip the proofs which will be published elsewhere. Suppose the spins on the upper base of the cylinder Ω are forced, by an external field, to be up and the spins on the lower base are forced to be down. Suppose we consider the model in th canonical ensemble in which the magnetization is fixed to be m = αm + (1 − α)(−m) = (2α − 1)m, 0 < α < 1. Finally suppose that, for a given spin configuration, we draw a line of length one at mid distance between every couple of nearest-neighbor opposite spins. A moment of reflection shows that, as a consequence of the assumed boundary condition, the set of lines thus obtained splits into several closed, disjoint, self-avoiding contours (). Then, once can prove that, picking up of the canonical ensemble a random configuration of spins, the set of contours γ0, γ1, . . . , γn associated with this configuration will be, with a probability tending to one as Ω → ∞ if β is large enough, such that |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://ipparco.roma1.infn.it/pagine/deposito/1967-1979/21-tensionesup.pdf |
| Alternate Webpage(s) | http://ipparco.roma1.infn.it/pagine/deposito/1967-1979/021-tensionesup1.pdf |
| Alternate Webpage(s) | http://ipparco.roma1.infn.it/pagine/deposito/1967-1979/tensionesup.pdf |
| Alternate Webpage(s) | http://141.108.20.11/pagine/deposito/1967-1979/tensionesup.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Assumed Coexist (image) Cylinder seal Integrated development environment Ising model Scientific Publication Single Linkage Cluster Analysis Spontaneous order Surface Tension Tension Headache |
| Content Type | Text |
| Resource Type | Article |
