Mesoscopic analysis of droplets in lattice systems with long-range Kac potentials

E. A. Carlen, R. Esposito, J. L. Lebowitz, R. Marra

Research output: Contribution to journalArticlepeer-review


We investigate the geometry of typical equilibrium configurations for a lattice gas in a finite macroscopic domain with attractive, long range Kac potentials. We focus on the case when the system is below the critical temperature and has a fixed number of occupied sites. We connect the properties of typical configurations to the analysis of the constrained minimizers of a mesoscopic non-local free energy functional, which we prove to be the large deviation functional for a density profile in the canonical Gibbs measure with prescribed global density. In the case in which the global density of occupied sites lies between the two equilibrium densities that one would have without a constraint on the particle number, a "droplet" of the high (low) density phase may or may not form in a background of the low (high) density phase. We determine the critical density for droplet formation, and the nature of the droplet, as a function of the temperature and the size of the system, by combining the present large deviation principle with the analysis of the mesoscopic functional given in Nonlinearity 22, 2919-2952 (2009).

Original languageEnglish (US)
Pages (from-to)221-237
Number of pages17
JournalActa Applicandae Mathematicae
Issue number1
StatePublished - Feb 2013

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


  • Critical droplet
  • Kac potential
  • Lattice systems


Dive into the research topics of 'Mesoscopic analysis of droplets in lattice systems with long-range Kac potentials'. Together they form a unique fingerprint.

Cite this