Phase Transitions for Dilute Particle Systems with Lennard-jones Potential
نویسندگان
چکیده
We consider a classical dilute particle system in a large box with pairinteraction given by a Lennard-Jones-type potential. The inverse temperature is picked proportionally to the logarithm of the particle density. We identify the free energy per particle in terms of a variational formula and show that this formula exhibits a cascade of phase transitions as the temperature parameter ranges from zero to infinity. Loosely speaking, the particle system separates into spatially distant components in such a way that within each phase all components are of the same size, which is the larger the lower the temperature. The main tool in our proof is a new large deviation principle for sparse point configurations. MSC 2000. Primary 82B21 Secondary 60F10; 60K35; 82B31; 82B05; 82B26.
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