Paulo C Lima
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
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In this contribution we discuss the role disordered (or random) systems have played in the study of non-Gibbsian measures. This role has two main aspects, the distinction between which has not always been fully clear: 1) {\em From} disordered systems: Disordered systems can be used as a tool; analogies with, as well as results and methods from the study of random systems can be employed to investigate non-Gibbsian properties of a variety of measures of physical and mathematical interest. 2) {\em Of} disordered systems: Non-Gibbsianness is a property of various (joint) measures describing quenc…
The Gibbs measures of a spin system on $Z^d$ with unbounded pair interactions $J_{xy} σ(x) σ(y)$ are studied. Here $\langle x, y \rangle \in E $, i.e. $x$ and $y$ are neighbors in $Z^d$. The intensities $J_{xy}$ and the spins $σ(x) , σ(y)$ are arbitrary real. To control their growth we introduce appropriate sets $J_q\subset R^E$ and $S_p\subset R^{Z^d}$ and prove that for every $J = (J_{xy}) \in J_q$: (a) the set of Gibbs measures $G_p(J)= \{μ: solves DLR, μ(S_p)=1\}$ is non-void and weakly compact; (b) each $μ\inG_p(J)$ obeys an integrability estimate, the same for all $μ$. Next we study the …
Boundary Free Energies, Quenched Mixing, and Gibbs-State Selection in Disordered Ising Models
该研究针对无序伊辛模型，证明了固定深度切向压力存在、吉布斯态选择独立性等结论，建立了全表面极限并给出反例，为相关统计物理问题提供了理论支撑。
For a broad class of Gaussian disordered systems at low temperature, we show that the Gibbs measure is asymptotically localized in small neighborhoods of a small number of states. From a single argument, we obtain (i) a version of "complete" path localization for directed polymers that is not available even for exactly solvable models; and (ii) a result about the exhaustiveness of Gibbs states in spin glasses not requiring the Ghirlanda-Guerra identities.
We consider a generic class of log-concave, possibly random, (Gibbs) measures. We prove the concentration of an infinite family of order parameters called multioverlaps. Because they completely parametrise the quenched Gibbs measure of the system, this implies a simple representation of the asymptotic Gibbs measures, as well as the decoupling of the variables in a strong sense. These results may prove themselves useful in several contexts. In particular in machine learning and high-dimensional inference, log-concave measures appear in convex empirical risk minimisation, maximum a-posteriori in…
Quantifying Gibbs measures of disordered crystals up to the solid-liquid phase transition
本文提出仅从沃罗诺伊胞重建热无序晶体晶格的方法，发现硅晶相存在四个概率一的大面，可作为固相吉布斯测度量化的关键特征。
We analyze the d-dimensional Blume-Emery-Griffiths model in the disordered region of parameters and we show that its free energy can be explicitly written in term of a series which is absolutely convergent at any temperature in an unbounded portion of this region. As a byproduct we also obtain an upper bound for the number of d-dimensional fixed polycubes of size n.
Disordered Gibbs measures and Gaussian conditioning
研究与高斯场相关的吉布斯测度下随机场分布，高温时通过特定条件从确定性界推概率界，低温时在\(k\)-RSB 球形自旋玻璃上用更精细条件设定得类似结果，还应用于统计物理两问题。
We consider the Gibbs-measures of continuous-valued height configurations on the $d$-dimensional integer lattice in the presence a weakly disordered potential. The potential is composed of Gaussians having random location and random depth; it becomes periodic under shift of the interface perpendicular to the base-plane for zero disorder. We prove that there exist localized interfaces with probability one in dimensions $d\geq 3+1$, in a `low-temperature' regime. The proof extends the method of continuous-to-discrete single- site coarse graining that was previously applied by the author for a do…
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。
The hard-core model has attracted much attention across several disciplines, representing lattice gases in statistical physics and independent sets in discrete mathematics and computer science. On finite graphs, we are given a parameter $λ$, and an independent set $I$ arises with probability proportional to $λ^{|I|}$. On infinite graphs a Gibbs measure is defined as a suitable limit with the correct conditional probabilities, and we are interested in determining when this limit is unique and when there is phase coexistence, i.e., existence of multiple Gibbs measures. It has long been conjectur…
Joint parameter estimations for spin glasses
本文证明在易于验证的条件下，二元极大伪似然估计量能对自旋玻璃模型的温度和外部场参数实现联合√N相合估计，涵盖Sherrington-Kirkpatrick模型及其稀释变体。
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