Absolute convergence of the free energy of the BEG model in the disordered region for all temperatures

Uniqueness of the Gibbs state of the BEG model in the disordered region of parameters

We show that the $d$-dimen\-sion\-al Blume-Emery-Griffiths model has a unique Gibbs state, for all temperature, in some portion of disordered region of parameters, ruling out the possibility of a reentrant behavior in the same

Lyapunov spectra for all symmetry classes of quasi-one-dimensional disordered systems of non-interacting Fermions

A random phase property is proposed for products of random matrices drawn from any one of the classical groups associated with the ten Cartan symmetry classes of non-interacting disordered Fermion systems. It allows to calculate the Lyapunov spectrum explicitly in a perturbative regime. These results apply to quasi-one-dimensional random Dirac operators which can be constructed as representatives for each of the ten symmetry classes. For those symmetry classes that correspond to two-dimensional topological insulators or superconductors, the random Dirac operators describing the one-dimensional…

方格上FAD三相点处的BEG模型

The BEG model at the FAD triple point on the square lattice

本文证明二维Blume-Emery-Griffiths模型在铁磁-反四极-无序三相点处任意温度下具有唯一吉布斯测度，从而建立无相变，证明基于随机簇表示与伯努利渗流耦合。

Absence of phase transitions in a class of integer spin systems

We exhibit a class of integer spin systems whose free energy can be written in term of an absolutely convergent series at any temperature. This class includes spin systems on $\Z^d$ interacting through infinite range pair potential polynomially decaying at large distances $r$ at a rate $1/r^{d+\e}$ with $\e>0$. It also contains the Blume-Emery-Griffiths model in the disordered phase at large values of the crystal field.

The disordered lattice free field pinning model approaching criticality

We continue the study, initiated in [Giacomin and Lacoin, JEMS 2018], of the localization transition of a lattice free field $ϕ=(ϕ(x))_{x \in Z^d}$, $d\ge 3$, in presence of a quenched disordered substrate. The presence of the substrate affects the interface at the spatial sites in which the interface height is close to zero. This corresponds to the Hamiltonian $$ \sum_{x\in Z^d }(βω_x+h)δ_x,$$ where $δ_x=1_{[-1,1]}(ϕ(x))$, and $(ω_x)_{x\in Z^d}$ is an IID centered field. A transition takes place when the average pinning potential $h$ goes past a threshold $h_c(β)$: from a delocalized phase $h…

FAD 和 AD 界面处的 Blume-Emery-Griffiths 模型

The Blume-Emery-Griffiths model at the FAD and AD interfaces

本文研究 BEG 模型在 FAD 与 AD 参数界面的零温及低温磁化，借助完美采样、Bernoulli 位点渗流耦合与匹配图比较，证明二维 FAD 磁化消失、关联指数衰减及 Gibbs 测度唯一，并改进 AD 界面结果。