Correlation Inequalities for Generalized Potts Model: General Griffiths' Inequalities
| dc.creator | Ganikhodjaev, Nasir | |
| dc.creator | Razak, Fatimah Abdul | |
| dc.date | 2007-07-26 | |
| dc.date.accessioned | 2026-07-07T08:20:24Z | |
| dc.date.available | 2026-07-07T08:20:24Z | |
| dc.description | In this paper, correlation inequalities which have been considered on Ising model are extended to q-Potts model. It is considered on generalized Potts model with interaction of any number of spins. We replace the set of spin values $F=\{1,2,..., q\}$ by the centered set $F=\{-(q-1)/2,-(q-3)/2,... ,(q-3)/2,(q-1)/2\}$. Let $N$ be the subset of one-dimensional lattice with $n$ vertices, $\g=(\s_1,\s_2,...,\s_n):N \to F^c$ be a configuration where ${(\s_i)}_\g$ is the number which appears as the ith spin (component) in $\g$ and $\s_i$ be a random variable whose value at $\g$ is ${(\s_i)}_\g$. Define $\s^R=\prod_{i \in R}\s_i$ for any list $R$ where any $i \in R$ implies that $i \in N$. We first prove that $<\s^R > \ge 0$ then we prove that for any two lists $R$ and $S$, we have $<\s^R \s^S >- < \s^R > < \s^S > \ge 0$. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0707.3848 | |
| dc.identifier | http://arxiv.org/abs/0707.3848 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135063 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Probability | |
| dc.subject | 82B20 | |
| dc.title | Correlation Inequalities for Generalized Potts Model: General Griffiths' Inequalities | |
| dc.type | text |