The McKean-Vlasov Equation in Finite Volume (2009)
Chayes, Lincoln, Panferov, Vladislav
We study the McKean--Vlasov equation on the finite tori of length scale $L$ in $d$--dimensions. We derive the necessary and sufficient conditions for the existence of a phase transition, which are...
Global existence and uniqueness of solutions to a model of price formation (2009)
Chayes, Lincoln, Gonzalez, Maria Del Mar, Gualdani, Maria Pia, Kim, Inwon
We study a model due to J.M. Lasry and P.L. Lions, describing the evolution of a scalar price which is realized as a free boundary in a 1-D diffusion equation with dynamically evolving, non-standard...
Colligative properties of solutions: I. Fixed concentrations, previous paper (2008)
Kenneth S. Alex, Marek Biskup, Lincoln Chayes
Using the formalism of rigorous statistical mechanics, we study the phenomena of phase separation and freezing-point depression upon freezing of solutions. Specifically, we devise an Ising-based...
LARGE-DEVIATIONS/THERMODYNAMIC APPROACH TO PERCOLATION ON THE COMPLETE GRAPH (2008)
Marek Biskup, Lincoln Chayes, S. Alex Smith
ABSTRACT. We present a large-deviations/thermodynamic approach to the classic problem of percolation on the complete graph. Specifically, we determine the large-deviation rate function for the...
Comment on a recent conjectured solution of the three-dimensional Ising model arXiv:0705.1045 (2008)
Wu, Fa Yueh, McCoy, Barry M., Fisher, Michael E., Chayes, Lincoln
In a recent paper published in the Philosophical Magazine [Z.-D. Zhang, Phil. Mag. 87, 5309-5419 (2007), arXiv:0705.1045], the author advances a conjectured solution for various properties of the...
Marek Biskup, Lincoln Chayes, Roman Kotecky
We study equilibrium droplets in two-phase systems at parameter values corresponding to phase coexistence. Specifically, we give a self-contained microscopic
LARGE-DEVIATIONS/THERMODYNAMIC APPROACH TO PERCOLATION ON THE COMPLETE GRAPH (2008)
Marek Biskup, Lincoln Chayes, S. Alex Smith
ABSTRACT. We present a large-deviations/thermodynamic approach to the classic problem of percolation on the complete graph. Specifically, we determine the large-deviation rate function for the...
The Phase Diagram of the Quantum Curie-Weiss Model (2008)
Chayes, Lincoln, Crawford, Nicholas, Ioffe, Dmitry, Levit, Anna
This paper studies a generalization of the Curie-Weiss model (the Ising model on a complete graph) to quantum mechanics. Using a natural probabilistic representation of this model, we give a complete...
A Two–Sided Contracting Stefan Problem (2008)
Abstract: We study a novel two–sided Stefan problem – motivated by the study of certain 2D interfaces – in which boundaries at both sides of the sample encroach into the bulk with rate equal to...
A Two–Sided Contracting Stefan Problem (2008)
Abstract: We study a novel two–sided Stefan problem – motivated by the study of certain 2D interfaces – in which boundaries at both sides of the sample encroach into the bulk with rate equal to...
Large Scale Properties of the IIIC for 2D Percolation (2007)
Chayes, Lincoln, Nolin, Pierre
We reinvestigate the 2D problem of the inhomogeneous incipient infinite cluster where, in an independent percolation model, the density decays to p_c with an inverse power, \lambda, of the distance...
Large Scale Properties of the IIIC for 2D Percolation (2007)
Chayes, Lincoln, Nolin, Pierre
We reinvestigate the 2D problem of the inhomogeneous incipient infinite cluster where, in an independent percolation model, the density decays to p_c with an inverse power, \lambda, of the distance...
Thinning of superfluid films below the critical point (2007)
Zandi, Roya, Shackell, Aviva, Rudnick, Joseph, Kardar, Mehran, Chayes, Lincoln
Experiments on $^4$He films reveal an attractive Casimir-like force at the bulk $\lambda$-point, and in the superfluid regime. Previous work has explained the magnitude of this force at the $\lambda$...
One dimensional nearest neighbor exclusion processes in inhomogeneous and random environments (2007)
Chayes, Lincoln, Liggett, Thomas M.
The processes described in the title always have reversible stationary distributions. In this paper, we give sufficient conditions for the existence of, and for the nonexistence of, nonreversible...
One Dimensional Nearest Neighbor Exclusion (2007)
Lincoln Chayes, Thomas M. Liggett
Abstract The processes described in the title always have reversible stationary distributions. In this paper, we give sufficient conditions for the existence of, and for the nonexistence of,...
One Dimensional Nearest Neighbor Exclusion (2007)
Lincoln Chayes, Thomas M. Liggett
Abstract. The processes described in the title always have reversible stationary distributions. In this paper, we give sufficient conditions for the existence of, and for the nonexistence of,...
On the absence of ferromagnetism in typical 2D ferromagnets (2006)
Biskup, Marek, Chayes, Lincoln, Kivelson, Steven A.
We consider the Ising systems in $d$ dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions which decay with a power, $s$, of the...
Marek Biskup, Lincoln Chayes, Nicholas Crawford
We consider a class of spin systems on Z d with vector valued spins (Sx) that interact via the pair-potentials Jx,y Sx · Sy. The interactions are generally spread-out in the sense that the Jx,y’s...
Quantum spin systems at positive temperature (2005)
Biskup, Marek, Chayes, Lincoln, Starr, Shannon
We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to...
Large-deviations/thermodynamic approach to percolation on the complete graph (2005)
Biskup, Marek, Chayes, Lincoln, Smith, S. Alex
We present a large-deviations/thermodynamic approach to the classic problem of percolation on the complete graph. Specifically, we determine the large-deviation rate function for the probability that...
Mean-field driven first-order phase transitions in systems with long-range interactions (2005)
Biskup, Marek, Chayes, Lincoln, Crawford, Nicholas
We consider a class of spin systems on $\Z^d$ with vector valued spins $(\bS_x)$ that interact via the pair-potentials $J_{x,y} \bS_x\cdot\bS_y$. The interactions are generally spread-out in the...
Marek Biskup, Lincoln Chayes, Shannon Starr
Abstract: We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be...
Colligative properties of solutions: I. Fixed concentrations (2004)
Alexander, Kenneth, Biskup, Marek, Chayes, Lincoln
Using the formalism of rigorous statistical mechanics, we study the phenomena of phase separation and freezing-point depression upon freezing of solutions. Specifically, we devise an Ising-based...
Colligative properties of solutions: II. Vanishing concentrations (2004)
Alexander, Kenneth, Biskup, Marek, Chayes, Lincoln
We continue our study of colligative properties of solutions initiated in math-ph/0407034. We focus on the situations where, in a system of linear size $L$, the concentration and the chemical...
S.A.: Order by disorder, without order, in a two-dimensional spin system with O(2)-symmetry (2004)
Marek Biskup, Lincoln Chayes, Steven A. Kivelson
Abstract. We present a rigorous proof of an ordering transition for a two-component two-dimensional antiferromagnet with nearest and next-nearest neighbor interactions. The low-temperature phase...
Colligative Properties of Solutions: II. Vanishing Concentrations (2004)
Kenneth S. Alex, Marek Biskup, Lincoln Chayes
We continue our study of colligative properties of solutions initiated in ref. 1. We focus on the situations where, in a system of linear size L, the concentration and the chemical potential scale...
Order by disorder, without order, in a two-dimensional spin system with O(2) symmetry (2003)
Biskup, Marek, Chayes, Lincoln, Kivelson, Steven A.
We present a rigorous proof of an ordering transition for a two-component two-dimensional antiferromagnet with nearest and next-nearest neighbor interactions. The low-temperature phase contains two...
Orbital ordering in transition-metal compounds: I. The 120-degree model (2003)
Biskup, Marek, Chayes, Lincoln, Nussinov, Zohar
We study the classical version of the 120-degree model. This is an attractive nearest-neighbor system in three dimensions with XY (rotor) spins and interaction such that only a particular projection...
Orbital order in classical models of transition-metal compounds (2003)
Nussinov, Zohar, Biskup, Marek, Chayes, Lincoln, Brink, Jeroen Van Den
We study the classical 120-degree and related orbital models. These are the classical limits of quantum models which describe the interactions among orbitals of transition-metal compounds. We...
Biskup, Marek, Chayes, Lincoln, Kotecky, Roman
We examine some aspects of the recent results by K. Binder. The equilibrium formation/dissolution of droplets in finite systems is discussed in the context of the canonical and the grand canonical...
A proof of the Gibbs-Thomson formula in the droplet formation regime (2003)
Biskup, Marek, Chayes, Lincoln, Kotecky, Roman
We study equilibrium droplets in two-phase systems at parameter values corresponding to phase coexistence. Specifically, we give a self-contained microscopic derivation of the Gibbs-Thomson formula...
Rigorous analysis of discontinuous phase transitions via mean-field bounds (2003)
Abstract: We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice Z d. Our essential assumption is that these models satisfy the condition of reflection...
Critical region for droplet formation in the two-dimensional Ising model (2002)
Biskup, Marek, Chayes, Lincoln, Kotecky, Roman
We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size $L^2$,...
Rigorous analysis of discontinuous phase transitions via mean-field bounds (2002)
Biskup, Marek, Chayes, Lincoln
We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice Z^d. Our essential assumption is that these models satisfy the condition of reflection...
On the formation/dissolution of equilibrium droplets (2002)
Biskup, Marek, Chayes, Lincoln, Kotecky, Roman
We consider liquid-vapor systems in finite volume $V\subset\R^d$ at parameter values corresponding to phase coexistence and study droplet formation due to a fixed excess $\delta N$ of particles above...
Phase transition and critical behavior in a model of organized criticality (2002)
Biskup, Marek, Blanchard, Philippe, Chayes, Lincoln, Gandolfo, Daniel, Krueger, Tyll
We study a model of ``organized'' criticality, where a single avalanche propagates through an \textit{a priori} static (i.e., organized) sandpile configuration. The latter is chosen according to an...
Mixed percolation as a bridge between site and bond percolation (2000)
Chayes, Lincoln, Schonmann, Roberto H.
By using mixed percolation as a bridge between site and bond percolation, we derive a new inequality between the critical points of these processes that is optimal in a certain sense.We also extend a...
New algorithm and results for the three-dimensional random field Ising Model (2000)
Machta, Jon, Newman, Mark, Chayes, Lincoln
The random field Ising model with Gaussian disorder is studied using a new Monte Carlo algorithm. The algorithm combines the advantanges of the replica exchange method and the two-replica cluster...
Sun, Rongfeng, Gould, Harvey, Machta, Jon, Chayes, Lincoln
Phase transitions of fluid mixtures of the type introduced by Stillinger and Helfand are studied using a continuum version of the invaded cluster algorithm. Particles of the same species do not...
Discontinuity of the magnetization in diluted O(n)-models (2000)
Lincoln Chayes, Senya B. Shlosman, Valentin A. Zagrebnov
We study the annealed site-diluted versions of the classical O(n) Heisenberg ferromagnets. It is shown that if the temperature is low enough, then at some value of the chemical potential there is...
Critical Behavior for 2d Uniform and Disordered Ferromagnets at Self-Dual Points (1998)
Chayes, Lincoln, Shtengel, Kirill
We consider certain two-dimensional systems with self--dual points including uniform and disordered $q$-state Potts models. For systems with continuous energy density (such as the disordered...
Parallel Invaded Cluster Algorithm for the Ising Model (1998)
Choi, Yongsoo, Machta, Jon, Tamayo, Pablo, Chayes, Lincoln
A parallel version of the invaded cluster algorithm is described. Results from large scale (up to 4096^2 and 512^3) simulations of the Ising model are reported. No evidence of critical slowing down...
Graphical representations and cluster algorithms for critical points with fields (1998)
Redner, Oliver, Machta, Jon, Chayes, Lincoln
A two-replica graphical representation and associated cluster algorithm is described that is applicable to ferromagnetic Ising systems with arbitrary fields. Critical points are associated with the...
No directed fractal percolation in zero area (1997)
Chayes, Lincoln, Pemantle, Robin, Peres, Yuval
We show that fractal (or "Mandelbrot") percolation in two dimensions produces a set containing no directed paths, when the set produced has zero area. This improves a similar result by the first...
Some problems in M intersect phi. (1983)
Thesis (Ph.D.)--Princeton University, 1983.