Critical Indices for Dyson's Asymptotically- Hierarchical Models

نویسنده

  • P. M. Bleher
چکیده

It is known that the investigation of the critical point for models of the type of Dyson's hierarchical models is reduced to the solution of some non-linear integral equation. In our previous publication the Gaussian solution was investigated. Here we construct non-Gaussian solutions of the equation and find the expressions for critical indices connected with them. Our procedure permits us to construct meaningful e-expansions. §

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Investigation of the Critical Point in Models of the Type of Dyson's Hierarchical Models

We consider the classical spin models where the Hamiltonians are small modifications of the Hamiltonians of Dyson's hierarchical models. Under some assumptions we investigate rigorously the neighbourhood of the critical point and find the critical indices. It follows that in the cases under consideration phenomenologicat Landau's theory of phase transitions is valid.

متن کامل

Renormalization of Dyson's Hierarchical Vector Valued φ Model at Low Temperatures

We investigate Dyson's hierarchical vector valued φ model at low temperatures. The case 2>c> j/2is considered. The pure phase is constructed, and the existence of its large scale limit is proved. The limit is Gaussian, but an unusual normalization has to be chosen. In the direction of the spontaneous magnetization one has to divide by the square root of the volume, but in the orthogonal directi...

متن کامل

A ug 1 99 6 U . of Iowa preprint 96 - 11 A Two - Parameter Recursion Formula For Scalar Field Theory

We present a two-parameter family of recursion formulas for scalar field theory. The first parameter is the dimension (D). The second parameter (ζ) allows one to continuously extrapolate between Wilson's approximate recur-sion formula and the recursion formula of Dyson's hierarchical model. We show numerically that at fixed D, the critical exponent γ depends continuously on ζ. We suggest the us...

متن کامل

Dyson’s equations for the (Ising) spin-glass

A complex problem is solved herej we show how to write Dyson's equations for trie (Ising) spin-glass that relate the propagator G ta trie mass operator M. In other words we are able to reduce trie inversion of an ultrametric matrix M to the solution of a Dyson's equation in ail sectors (for the replicon sectcr trie result had already been derived). It turns oui that what renders the problem tra...

متن کامل

Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth

In this paper‎, ‎we consider the following Kirchhoff-type equations‎: ‎$-‎left(a+bint_{mathbb{R}^{3}}|nabla u|^{2}right)Delta u+V(x) u=lambda$ $f(x,u)+u^{5}‎, ‎quad mbox{in }mathbb{R}^{3},$ ‎$u(x)>0‎, ‎quad mbox{in }mathbb{R}^{3},$ ‎$uin H^{1}(mathbb{R}^{3})‎ ,‎$ ‎ ‎‎‎where $a,b>0$ are constants and $lambda$ is a positive parameter‎. ‎The aim of this paper is to study the existence of positive ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005