What question did this study set out to answer?

Determine large deviation principles, central limit theorems, and explicit convergence rates for block magnetization vectors in generalized block spin mean-field Ising models.

February 1, 2020Journal of Statistical PhysicsOpen Access

Fluctuation Results for General Block Spin Ising Models

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Authors

HKHolger KnöpfelUniversity of Münster MLMatthias LöweAugsburg University KSKristina SchubertTU Dortmund University

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Implication

Theoretical analysis demonstrates limit theorems and convergence rates for block spin Ising models, highlighting fluctuation behaviors in multi-group mean-field systems.

Key Points

Determine large deviation principles, central limit theorems, and explicit convergence rates for block magnetization vectors in generalized block spin mean-field Ising models.
Analyzed an Ising model where vertices are partitioned into a finite collection of blocks with fixed proportions and block-dependent interaction matrices.
Applied the exchangeable pair approach within Stein's method to evaluate rates of convergence in the high-temperature regime.
Proved Large Deviation Principles and Central Limit Theorems for the vector of block magnetizations under general interaction matrix conditions.
Established an explicit rate of convergence for the Central Limit Theorem governing the block magnetization vector in the high-temperature regime.

Cite This Study

Knöpfel et al. (2020) studied this question.

synapsesocial.com/papers/69dc5e833080d3567e274fc7 https://doi.org/10.1007/s10955-020-02489-0

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Implication

Theoretical analysis demonstrates limit theorems and convergence rates for block spin Ising models, highlighting fluctuation behaviors in multi-group mean-field systems.

Fluctuation Results for General Block Spin Ising Models

Discussion

Member takes

Implication

Key Points

Cite This Study

Fluctuation Results for General Block Spin Ising Models

Discussion

Member takes

Implication

Key Points

Cite This Study

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