Metropolis algorithm and equienergy sampling for two mean field spin systems
| dc.creator | Federico, Bassetti | |
| dc.creator | Fabrizio, Leisen | |
| dc.date | 2007-04-06 | |
| dc.date | 2007-05-08 | |
| dc.date.accessioned | 2026-07-07T07:59:54Z | |
| dc.date.available | 2026-07-07T07:59:54Z | |
| dc.description | In this paper we study the Metropolis algorithm in connection with two mean--field spin systems, the so called mean--field Ising model and the Blume--Emery--Griffiths model. In both this examples the naive choice of proposal chain gives rise, for some parameters, to a slowly mixing Metropolis chain, that is a chain whose spectral gap decreases exponentially fast (in the dimension $N$ of the problem). Here we show how a slight variant in the proposal chain can avoid this problem, keeping the mean computational cost similar to the cost of the usual Metropolis. More precisely we prove that, with a suitable variant in the proposal, the Metropolis chain has a spectral gap which decreases polynomially in 1/N. Using some symmetry structure of the energy, the method rests on allowing appropriate jumps within the energy level of the starting state. | |
| dc.identifier | https://arxiv.org/abs/0704.0906 | |
| dc.identifier | http://arxiv.org/abs/0704.0906 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128542 | |
| dc.subject | Probability | |
| dc.subject | Statistics Theory | |
| dc.subject | Computation | |
| dc.title | Metropolis algorithm and equienergy sampling for two mean field spin systems | |
| dc.type | text |