The magnetization at high temperature for a p-spin interaction model with external field

David Márquez-Carreras

Displaying similar documents to “The magnetization at high temperature for a p-spin interaction model with external field”

On the number of ground states of the Edwards–Anderson spin glass model

Louis-Pierre Arguin, Michael Damron (2014)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

Ground states of the Edwards–Anderson (EA) spin glass model are studied on infinite graphs with finite degree. Ground states are spin configurations that locally minimize the EA Hamiltonian on each finite set of vertices. A problem with far-reaching consequences in mathematics and physics is to determine the number of ground states for the model on $ℤ^{d}$ for any $d$ . This problem can be seen as the spin glass version of determining the number of infinite geodesics in first-passage percolation...

Random hysteresis loops

Gioia Carinci (2013)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

Dynamical hysteresis is a phenomenon which arises in ferromagnetic systems below the critical temperature as a response to adiabatic variations of the external magnetic field. We study the problem in the context of the mean-field Ising model with Glauber dynamics, proving that for frequencies of the magnetic field oscillations of order $N^{- 2 / 3}$ , $N$ the size of the system, the “critical” hysteresis loop becomes random.

Local well-posedness for a two-phase model with magnetic field and vacuum

Xiuhui Yang (2021)

Applications of Mathematics

Similarity:

This paper proves the local well-posedness of strong solutions to a two-phase model with magnetic field and vacuum in a bounded domain $Ω \subset ℝ^{3}$ without the standard compatibility conditions.

The discrete-time parabolic Anderson model with heavy-tailed potential

Francesco Caravenna, Philippe Carmona, Nicolas Pétrélis (2012)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed $(1 + d)$ -dimensional polymer interacting with a random potential, which is constant in the deterministic direction and i.i.d. in the $d$ orthogonal directions. The potential at each site is a positive random variable with a polynomial tail at infinity. We show that, as the size of the system diverges, the polymer extremity is localized almost surely at one single point which grows...

A spatial individual-based contact model with age structure

Dominika Jasińska (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

The Markov dynamics of an infinite continuum birth-and-death system of point particles with age is studied. Each particle is characterized by its location $x \in ℝ^{d}$ and age $a_{x} \geq 0$ . The birth and death rates of a particle are age dependent. The states of the system are described in terms of probability measures on the corresponding configuration space. The exact solution of the evolution equation for the correlation functions of first and second orders is found.

Invariance principle for the random conductance model with dynamic bounded conductances

Sebastian Andres (2014)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

We study a continuous time random walk $X$ in an environment of dynamic random conductances in $ℤ^{d}$ . We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched invariance principle for $X$ , and obtain Green’s functions bounds and a local limit theorem. We also discuss a connection to stochastic interface models.

Particles in the superworldline and BRST

Eugenia Boffo (2022)

Archivum Mathematicum

Similarity:

In this short note we discuss $N$ -supersymmetric worldlines of relativistic massless particles and review the known result that physical spin- $N / 2$ fields are in the first BRST cohomology group. For $N = 1, 2, 4$ , emphasis is given to particular deformations of the BRST differential, that implement either a covariant derivative for a gauge theory or a metric connection in the target space seen by the particle. In the end, we comment about the possibility of incorporating Ramond-Ramond fluxes in the background. ...

Existentially closed II₁ factors

Ilijas Farah, Isaac Goldbring, Bradd Hart, David Sherman (2016)

Fundamenta Mathematicae

Similarity:

We examine the properties of existentially closed ( $^{ω}$ -embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed ( $^{ω}$ -embeddable) II₁ factor is approximately inner to prove that Th() is not model-complete. We also show that Th() is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th().

Chaotic behaviour of continuous dynamical system generated by Euler equation branching and its application in macroeconomic equilibrium model

Barbora Volná (2015)

Mathematica Bohemica

Similarity:

We focus on the special type of the continuous dynamical system which is generated by Euler equation branching. Euler equation branching is a type of differential inclusion $\dot{x} \in {f (x), g (x)}$ , where $f, g : X \subset ℝ^{n} \to ℝ^{n}$ are continuous and $f (x) \neq g (x)$ at every point $x \in X$ . It seems this chaotic behaviour is typical for such dynamical system. In the second part we show an application in a new formulated overall macroeconomic equilibrium model. This new model is based on the fundamental macroeconomic aggregate equilibrium model called...

Uniform regularity for an isentropic compressible MHD- $P 1$ approximate model arising in radiation hydrodynamics

Tong Tang, Jianzhu Sun (2021)

Czechoslovak Mathematical Journal

Similarity:

It is well known that people can derive the radiation MHD model from an MHD- $P 1$ approximate model. As pointed out by F. Xie and C. Klingenberg (2018), the uniform regularity estimates play an important role in the convergence from an MHD- $P 1$ approximate model to the radiation MHD model. The aim of this paper is to prove the uniform regularity of strong solutions to an isentropic compressible MHD- $P 1$ approximate model arising in radiation hydrodynamics. Here we use the bilinear commutator and...

On the geometry of proportional quotients of $l ₁^{m}$

Piotr Mankiewicz, Stanisław J. Szarek (2003)

Studia Mathematica

Similarity:

We compare various constructions of random proportional quotients of $l ₁^{m}$ (i.e., with the dimension of the quotient roughly equal to a fixed proportion of m as m → ∞) and show that several of those constructions are equivalent. As a consequence of our approach we conclude that the most natural “geometric” models possess a number of asymptotically extremal properties, some of which were hitherto not known for any model.

Spin representations and binary numbers

Henrik Winther (2024)

Archivum Mathematicum

Similarity:

We consider a construction of the fundamental spin representations of the simple Lie algebras $𝔰𝔬 (n)$ in terms of binary arithmetic of fixed width integers. This gives the spin matrices as a Lie subalgebra of a $ℤ$ -graded associative algebra (rather than the usual $ℕ$ -filtered Clifford algebra). Our description gives a quick way to write down the spin matrices, and gives a way to encode some extra structure, such as the real structure which is invariant under the compact real form, for some $n$ ....

A geometric point of view on mean-variance models

Piotr Jaworski (2003)

Applicationes Mathematicae

Similarity:

This paper deals with the mathematics of the Markowitz theory of portfolio management. Let E and V be two homogeneous functions defined on ℝⁿ, the first linear, the other positive definite quadratic. Furthermore let Δ be a simplex contained in ℝⁿ (the set of admissible portfolios), for example Δ : x₁+ ... + xₙ = 1, $x_{i} \geq 0$ . Our goal is to investigate the properties of the restricted mappings (V,E):Δ → ℝ² (the so called Markowitz mappings) and to classify them. We introduce the notion of a...

Odd cutsets and the hard-core model on $ℤ^{d}$

Ron Peled, Wojciech Samotij (2014)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

We consider the hard-core lattice gas model on $ℤ^{d}$ and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds $C d^{- 1 / 3} {(log d)}^{2}$ , the model exhibits multiple hard-core measures, thus improving the previous bound of $C d^{- 1 / 4} {(log d)}^{3 / 4}$ given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in $ℤ^{d}$ , the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined...

On the structure of the set of higher order spreading models

Bünyamin Sarı, Konstantinos Tyros (2014)

Studia Mathematica

Similarity:

We generalize some results concerning the classical notion of a spreading model to spreading models of order ξ. Among other results, we prove that the set $S M_{ξ}^{w} (X)$ of ξ-order spreading models of a Banach space X generated by subordinated weakly null ℱ-sequences endowed with the pre-partial order of domination is a semilattice. Moreover, if $S M_{ξ}^{w} (X)$ contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if $S M_{ξ}^{w} (X)$ is uncountable, then it contains an antichain...

Stein’s method in high dimensions with applications

Adrian Röllin (2013)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

Let $h$ be a three times partially differentiable function on $ℝ^{n}$ , let $X = (X_{1}, ..., X_{n})$ be a collection of real-valued random variables and let $Z = (Z_{1}, ..., Z_{n})$ be a multivariate Gaussian vector. In this article, we develop Stein’s method to give error bounds on the difference $𝔼 h (X) - 𝔼 h (Z)$ in cases where the coordinates of $X$ are not necessarily independent, focusing on the high dimensional case $n \to \infty$ . In order to express the dependency structure we use Stein couplings, which allows for a broad range of applications, such as classic...

On the $L^{p}$ index of spin Dirac operators on conical manifolds

André Legrand, Sergiu Moroianu (2006)

Studia Mathematica

Similarity:

We compute the index of the Dirac operator on a spin Riemannian manifold with conical singularities, acting from $L^{p} (Σ ⁺)$ to $L^{q} (Σ ¯)$ with p,q > 1. When 1 + n/p - n/q > 0 we obtain the usual Atiyah-Patodi-Singer formula, but with a spectral cut at (n+1)/2 - n/q instead of 0 in the definition of the eta invariant. In particular we reprove Chou’s formula for the L² index. For 1 + n/p - n/q ≤ 0 the index formula contains an extra term related to the Calderón projector.