Limit Theorems for the Bipartite Potts Model

Liu, Qun

doi:10.1007/s10955-020-02655-4

Cited by 8 publications

(14 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us mention at this point that, while we were finishing the current manuscript we learned that in [29] the author studies a very similar model: Here the number of blocks is restricted to two, but they may be of different size. His techniques, however are different from ours.…”

Section: Introductionmentioning

confidence: 98%

Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model

Knöpfel

Löwe

Sambale

2021

Electron. Commun. Probab.

View full text Add to dashboard Cite

We introduce and analyze a generalization of the blocks spin Ising (Curie-Weiss) models that were discussed in a number of recent articles. In these block spin models each spin in one of s blocks can take one of a finite number of q ≥ 3 values or colors, hence the name block spin Potts model. We prove a large deviation principle for the percentage of spins of a certain color in a certain block. These values are represented in an s × q matrix. We show that for uniform block sizes there is a phase transition. In some regime the only equilibrium is the uniform distribution of all colors in all blocks, while in other parameter regimes there is one predominant color, and this is the same color with the same frequency for all blocks. Finally, we establish log-Sobolev-type inequalities for the block spin Potts model.

show abstract

Section: Introductionmentioning

confidence: 98%

Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model

Knöpfel

Löwe

Sambale

2021

Electron. Commun. Probab.

View full text Add to dashboard Cite

show abstract

“…For s = 2, Theorem 1 is an explicit version of [21,Theorem 2] and the limiting distribution coincides. However, it is not apparent from [21] that the limiting distribution is degenerate, which we shall circumvent in the following.…”

Section: Remarkmentioning

confidence: 96%

“…The main goal of the present note is to prove a Central Limit Theorem (CLT, for short) for this order parameter (the block magnetization) in the high-temperature regime. Notice that Theorem 2 in [21] studies a similar question. However, there only two blocks are allowed (which makes the situation technically considerably easier) and little is known about the parameter regime where the CLT holds.…”

Section: Introductionmentioning

confidence: 93%

“…In [19] and [21] for the first time block spin models with three or more possible spin values were considered. They are natural extensions of mean-field Potts models as considered as a generalization of the Curie-Weiss model in [16] and [11].…”

Section: Introductionmentioning

confidence: 99%

“…They are natural extensions of mean-field Potts models as considered as a generalization of the Curie-Weiss model in [16] and [11]. In [21] the author discusses the situation of a block spin Potts model 1 with two blocks or groups and proves limit theorems for this situation. In [19] on the other hand, a setting with several groups is analyzed, however, these have to have an equal size.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fluctuations of the Magnetization in the Block Potts Model

2022

View full text Add to dashboard Cite

In this note we study the block spin mean-field Potts model, in which the spins are divided into s blocks and can take $$q\ge 2$$ q ≥ 2 different values (colors). Each block is allowed to contain a different proportion of vertices and behaves itself like a mean-field Ising/Potts model which also interacts with other blocks according to different temperatures. Of particular interest is the behavior of the magnetization, which counts the number of colors appearing in the distinct blocks. We prove central limit theorems for the magnetization in the generalized high-temperature regime and provide a moderate deviation principle for its fluctuations on lower scalings. More precisely, the magnetization concentrates around the uniform vector of all colors with an explicit, but singular, Gaussian distribution. In order to remove the singular component, we will also consider a rotated magnetization, which enables us to compare our results to various related models.

show abstract

Energy Landscape of the Two-Component Curie–Weiss–Potts Model with Three Spins

Kim

2022

J Stat Phys

View full text Add to dashboard Cite

Limit Theorems for the Bipartite Potts Model

Cited by 8 publications

References 15 publications

Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model

Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model

Fluctuations of the Magnetization in the Block Potts Model

Energy Landscape of the Two-Component Curie–Weiss–Potts Model with Three Spins

Contact Info

Product

Resources

About