Publications associées à Random cluster model

Metastability of the Potts Ferromagnet on Random Regular Graphs

We study the performance of Markov chains for the q-state ferromagnetic Potts model on random regular graphs. While the cases of the grid and the complete graph are by now well-understood, the case of random regular graphs has resisted a detailed analysis ...

SPRINGER2023

Conformal Field Theory at the Lattice Level: Discrete Complex Analysis and Virasoro Structure

Clément Hongler

Critical statistical mechanics and Conformal Field Theory (CFT) are conjecturally connected since the seminal work of Beliavin et al. (Nucl Phys B 241(2):333-380, 1984). Both exhibit exactly solvable structures in two dimensions. A long-standing question ( ...

SPRINGER2022

Nonperturbative Quantum Field Theory in Curved Spacetime

Kamran Salehi Vaziri

Quantum Field Theory(QFT) as one of the most promising frameworks to study high energy and condensed matter physics, has been mostly developed by perturbative methods. However, perturbative methods can only capture a small island of the space of QFTs. QFT ...

EPFL2022

Tensor network investigation of frustrated Ising models

Jeanne Colbois

In spin systems, geometrical frustration describes the impossibility of minimizing simultaneously all the interactions in a Hamiltonian, often giving rise to macroscopic ground-state degeneracies and emergent low-temperature physics. In this thesis, combin ...

EPFL2022

Solving frustrated Ising models using tensor networks

Frédéric Mila, Jeanne Colbois

Motivated by the recent success of tensor networks to calculate the residual entropy of spin ice and kagome Ising models, we develop a general framework to study frustrated Ising models in terms of infinite tensor networks that can be contracted using stan ...

2021

Emergence of Concentration Effects in the Variational Analysis of the N-Clock Model

Matthias Ruf, Matthias Benjamin Ruf

We investigate the relationship between the N-clock model (also known as planar Potts model or DOUBLE-STRUCK CAPITAL ZN-model) and the XY model (at zero temperature) through a Gamma-convergence analysis of a suitable rescaling of the energy as both the num ...

WILEY2022

Imaginary Multiplicative Chaos: Moments, Regularity And Connections To The Ising Model

Janne Matias Junnila

In this article we study imaginary Gaussian multiplicative chaos-namely a family of random generalized functions which can formally be written as e(iX(x)), where X is a log-correlated real-valued Gaussian field on R-d, that is, it has a logarithmic singula ...

INST MATHEMATICAL STATISTICS2020

Critical scaling for an anisotropic percolation system on Z(2)

Thomas Mountford, Hao Xue

In this article, we consider an anisotropic finite-range bond percolation model on Z(2). On each horizontal layer {(x, i): x is an element of Z} we have edges for 1

2020

Two-dimensional O(n) models and logarithmic CFTs

Bernardo Zan, Victor Gorbenko

We study O(n)-symmetric two-dimensional conformal field theories (CFTs) for a continuous range of n below two. These CFTs describe the fixed point behavior of self-avoiding loops. There is a pair of known fixed points connected by an RG flow. When n is equ ...

Springer Nature2020

The Scaling Limit Of Critical Ising Interfaces Is Cle3

Clément Hongler

In this paper, we consider the set of interfaces between + and - spins arising for the critical planar Ising model on a domain with + boundary conditions, and show that it converges to nested CLE3. ...

INST MATHEMATICAL STATISTICS2019

Ising Model: Local Spin Correlations and Conformal Invariance

Clément Hongler, Sung Chul Park

We study the 2-dimensional Ising model at critical temperature on a simply connected subset of the square grid Z2. The scaling limit of the critical Ising model is conjectured to be described by Conformal Field Theory; in particular, there is expected to b ...

Springer2019

Walking, weak first-order transitions, and complex CFTs

Bernardo Zan, Victor Gorbenko

We discuss walking behavior in gauge theories and weak first-order phase transitions in statistical physics. Despite appearing in very different systems (QCD below the conformal window, the Potts model, deconfined criticality) these two phenomena both impl ...

Springer Nature2018

Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at Q > 4

Bernardo Zan, Victor Gorbenko

We study complex CFTs describing fixed points of the two-dimensional Q-state Potts model with Q > 4. Their existence is closely related to the weak first-order phase transition and the "walking" renormalization group (RG) behavior present in the real Potts ...

2018

Magnetic-Order Crossover in Coupled Spin Ladders

We report a novel crossover behavior in the long-range-ordered phase of a prototypical spin-1/2 Heisenberg antiferromagnetic ladder compound (C7H10N)(2)CuBr4. The staggered order was previously evidenced from a continuous and symmetric splitting of (NNMR)- ...

American Physical Society2017

Conformal invariance of crossing probabilities for the Ising model with free boundary conditions

Clément Hongler

We prove that crossing probabilities for the critical planar Ising model with free boundary conditions are conformally invariant in the scaling limit, a phenomenon first investigated numerically by Langlands, Lewis and Saint-Aubin (J. Stat. Phys. 98 (2000) ...

Inst Mathematical Statistics2016

Topological Aspects of Symmetry Breaking in Triangular-Lattice Ising Antiferromagnets

Frédéric Mila, Andrew James Smerald

Using a specially designed Monte Carlo algorithm with directed loops, we investigate the triangular lattice Ising antiferromagnet with coupling beyond the nearest neighbors. We show that the first-order transition from the stripe state to the paramagnet ca ...

2016

Phase diagram of diluted Ising ferromagnet LiHoxY1-xF4

Henrik Moodysson Rønnow, Peter Babkevich, Bastien Dalla Piazza, Julian Piatek, Neda Nikseresht Ghanepour, Conradin Kraemer, Ivan Kovacevic

We present a systematic study of the phase diagram of LiHoxY1-xF4 (0.25

Amer Physical Soc2016

Conformal Invariance of Spin Correlations in the Planar Ising Model

Clément Hongler

We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming fro ...

2015

Modeling of percolation of globular-equiaxed grains in Al-Cu alloys

Michel Rappaz, Jean-Luc Desbiolles, Christophe Mondoux

A new mesoscopic model able to describe percolation of globular-equiaxed grains, highly relevant for hot tearing formation in castings, has been developed. This model is inspired from the granular model of Sistaninia et al. [1-5] that considers polyhedral ...

Iop Publishing Ltd2015

Bond Graph Model Representation of a New Reciprocating Finned Air Compressor

Alfred Rufer, Mahbod Heidari

A new finned reciprocating air compressor model is developed recently for compressed air energy storage. First the mechanism of operation of the new compressor is described. The complexity of the design encouraged us to develop the model based on the bond ...

2014