Thermodynamic Limit for Mean-Field Spin Models

Details Thermodynamic Limit for Mean-Field Spin Models Thermodynamic Limit for Mean-Field Spin Models

2003-11-11

arxiv.org/abs/math-ph/0311017v2

Physics

Mathematical Physics

15 pages, few improvements. To appear in MPEJ

Scientific paper

If the Boltzmann-Gibbs state $\omega_N$ of a mean-field $N$-particle system with Hamiltonian $H_N$ verifies the condition $$ \omega_N(H_N) \ge \omega_N(H_{N_1}+H_{N_2}) $$ for every decomposition $N_1+N_2=N$, then its free energy density increases with $N$. We prove such a condition for a wide class of spin models which includes the Curie-Weiss model, its p-spin generalizations (for both even and odd p), its random field version and also the finite pattern Hopfield model. For all these cases the existence of the thermodynamic limit by subadditivity and boundedness follows.

Affiliated with

Also associated with

No associations

Rating

Thermodynamic Limit for Mean-Field Spin Models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Thermodynamic Limit for Mean-Field Spin Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Thermodynamic Limit for Mean-Field Spin Models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-421814