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The Crossover Region Between Long-Range and Short-Range Interactions for the Critical Exponents
, 2014It is well know that systems with an interaction decaying as a power of the distance may have critical exponents that are different from those of short-range systems.
É. Brézin+2 more
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Critical conductivity exponent for Si:B
Physical Review Letters, 1991We have determined the critical exponent which characterizes the approach of the zero-temperature conductivity to the insulating phase from measurements down to 60 mK of the resistivity of a series of just-metallic uncompensated p-type Si:B samples with dopant concentrations near the critical concentration for the metal-insulator transition.
Youzhu Zhang+2 more
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Ising Critical Exponents on Random Trees and Graphs
Communications in Mathematical Physics, 2012We study the critical behavior of the ferromagnetic Ising model on random trees as well as so-called locally tree-like random graphs. We pay special attention to trees and graphs with a power-law offspring or degree distribution whose tail behavior is ...
S. Dommers, C. Giardinà, R. Hofstad
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Paramagnetic critical exponents
Physica B+C, 1988Abstract Critical point exponents for the paramagnetic susceptibility in Co and Fe have been derived from the measurements published by Develey. The exponent, γ, for the linear reduced temperature (1 - T/Tc) is the same as that for the non-linear reduced temperature (1 − Tc/T).
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Surface Critical Exponents in Terms of Bulk Exponents
Physical Review Letters, 1977The surface exponents associated with critical phenomena in semi-infinite systems are derived exactly in terms of bulk exponents. Results are ${\ensuremath{\gamma}}_{1,1}=\ensuremath{\nu}\ensuremath{-}1$, ${\ensuremath{\gamma}}_{1}=\ensuremath{\nu}+\frac{(\ensuremath{\gamma}\ensuremath{-}1)}{2}$, ${\ensuremath{\beta}}_{1}=\frac{(3\ensuremath ...
M. A. Moore, A. J. Bray
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Inequalities for critical exponents
1992The principal goal of the theory of critical phenomena is to make quantitative predictions for universal features of critical behavior — critical exponents, universal ratios of critical amplitudes, equations of state, and so forth — as discussed in Section 1.1. (Non-universal features, such as critical temperatures, are of lesser interest.) The present
Roberto Fernández+2 more
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Norms possessing a critical exponent
Ukrainian Mathematical Journal, 1987The critical exponent of a norm in \(R^ n\) is defined as the minimal natural number q such that for all linear operators satisfying \(\| A\| =1\), the equality \(\| A^ q\| =1\) implies \(\| A^ m\| =1\) for \(m>q\). The existence and nonexistence of the critical exponent is considered from the point of view of the theory of analytic functions of ...
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A Nonlinear Elliptic PDE with Two Sobolev–Hardy Critical Exponents
, 2011In this paper, we consider the following PDE involving two Sobolev–Hardy critical exponents, $$ \label{0.1}\left\{\begin{aligned}& \Delta u + \lambda\frac{u^{2^*(s_1)-1}}{|x|^{s_1}} + \frac{u^{2^*(s_2)-1}}{|x|^{s_2}} =0 \quad \rm {in}\,\,\Omega,\quad ...
Yanyan Li, Changshou Lin
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Critical exponents for the restricted sandpile
Physical Review E, 2006I report large-scale Monte Carlo studies of a one-dimensional height-restricted stochastic sandpile using the quasistationary simulation method. Results for systems of up to 50 000 sites yield estimates for critical exponents that differ significantly from those obtained using smaller systems, but are consistent with recent predictions derived from a ...
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1993
Publisher Summary This chapter discusses critical exponents and explains the concept of Hilbert space. The notion of the critical exponent of a Banach space has its origin in considerations concerning convergence of the iterative process. The theory of critical exponent of a polytope is essentially combinatorial.
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Publisher Summary This chapter discusses critical exponents and explains the concept of Hilbert space. The notion of the critical exponent of a Banach space has its origin in considerations concerning convergence of the iterative process. The theory of critical exponent of a polytope is essentially combinatorial.
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