Mass Scaling of the Near-Critical 2D Ising Model Using Random Currents

@article{Klausen2022MassSO,
  title={Mass Scaling of the Near-Critical 2D Ising Model Using Random Currents},
  author={Frederik Ravn Klausen and Aran Raoufi},
  journal={Journal of Statistical Physics},
  year={2022}
}
We examine the Ising model at its critical temperature with an external magnetic field ha 15 8 on aZ for a, h > 0. A new proof of exponential decay of the truncated two-point correlation functions is presented. It is proven that the mass (inverse correlation length) is of the order of h 8 15 in the limit h → 0. This was previously proven with CLE-methods in [1]. Our new proof uses instead the random current representation of the Ising model and its backbone exploration. The method further… 
View PDF on arXiv
2 Citations
Background Citations
2
Methods Citations
1

2 Citations

Citation Type

Citation Type

The Gaussian process for particle masses in the near-critical Ising model
Abstract. We review the construction of a stationary Gaussian process X(t) starting from the near-critical continuum scaling limit Φ of the Ising magnetization and its relation to the mass spectrum…
Strict monotonicity, continuity and bounds on the Kert\'{e}sz line for the random-cluster model on $\mathbb{Z}^d$
Ising and Potts models can be studied using the Fortuin–Kasteleyn representation through the Edwards-Sokal coupling. This adapts to the setting where the models are exposed to an external field of…

References

SHOWING 1-10 OF 43 REFERENCES
Exponential Decay for the Near‐Critical Scaling Limit of the Planar Ising Model
We consider the Ising model at its critical temperature with external magnetic field ha15/8 on the square lattice with lattice spacing a. We show that the truncated two‐point function in this model…
Marginal triviality of the scaling limits of critical 4D Ising and 𝜑44 models
We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A similar…
Critical amplitudes and mass spectrum of the 2d Ising model in a magnetic field
Emergent planarity in two-dimensional Ising models with finite-range Interactions
The known Pfaffian structure of the boundary spin correlations, and more generally order–disorder correlation functions, is given a new explanation through simple topological considerations within…
Random currents expansion of the Ising model
Critical behavior at an order/disorder phase transition has been a central object of interest in statistical physics. In the past century, techniques borrowed from many different fields of…
The phase transition in a general class of Ising-type models is sharp
For a family of translation-invariant, ferromagnetic, one-component spin systems—which includes Ising and ϕ4 models—we prove that (i) the phase transition is sharp in the sense that at zero magnetic…
Random Currents and Continuity of Ising Model’s Spontaneous Magnetization
The spontaneous magnetization is proved to vanish continuously at the critical temperature for a class of ferromagnetic Ising spin systems which includes the nearest neighbor ferromagnetic Ising spin…
Lace Expansion for the Ising Model
The lace expansion has been a powerful tool for investigating mean-field behavior for various stochastic-geometrical models, such as self-avoiding walk and percolation, above their respective…
Conformal Measure Ensembles for Percolation and the FK–Ising Model
Under some general assumptions, we construct the scaling limit of open clusters and their associated counting measures in a class of two dimensional percolation models. Our results apply, in…
Planar Ising magnetization field I. Uniqueness of the critical scaling limit
The aim of this paper is to prove the following result. Consider the critical Ising model on the rescaled grid $a\mathbb{Z}^2$, then the renormalized magnetization field \[\Phi^a:=a^{15/8}\sum_{x\in…
...
...