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 ...
We develop techniques to study the phase transition for planar Gaussian percolation models that are not (necessarily) positively correlated. These models lack the property of positive associations (also known as the 'FKG inequality'), and hence many classi ...
We study the asymptotic behavior of the N-clock model, a nearest neighbors ferromagnetic spin model on the d-dimensional cubic epsilon-lattice in which the spin field is constrained to take values in a discretization S-N of the unit circle S-1 consisting o ...
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 ( ...
This thesis is motivated by recent experiments on systems described by extensions of the one-dimensional transverse-field Ising (TFI) model where (1) finite-size properties of Ising-ordered phases -- specifically, ground state level crossings -- were obser ...
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 ...
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
In this thesis, we consider an anisotropic finite-range bond percolation model on Z2. On each horizontal layer {(x,i):x∈Z} for i∈Z, we have edges ⟨(x,i),(y,i)⟩ for 1≤∣x−y∣≤N with $N\in\mathbb{N ...
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 ...
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. ...
