Resistance Training for Special Populations

Rieger, Brian W.; Roitman, Jeffrey L.

doi:10.1519/1533-4295(1999)021<0061:rtfsp>2.0.co;2

Cited by 7 publications

(16 citation statements)

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“…His predictions were checked numerically by several authors, using the mapping of the RTIC onto a free fermion model, 13 density-matrix renormalization group 14 (DMRG) or quantum Monte Carlo. 15 Critical exponents calculated numerically were found in good agreement with Fisher's results. The renormalization scheme of Fisher was also applied to the q-state disordered Potts chain by Senthil and Majumdar; 16 they found that the critical behavior does not depend on q, therefore all critical exponents should be identical to those of the RTIC obtained by Fisher and corresponding to the case q = 2.…”

Section: Introductionsupporting

confidence: 79%

Critical behavior of the random Potts chain

Carlon¹,

Chatelain²,

Berche³

1999

Phys. Rev. B

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We study the critical behavior of the random q-state Potts quantum chain by density matrix renormalization techniques. Critical exponents are calculated by scaling analysis of finite lattice data of short chains (L ≤ 16) averaging over all possible realizations of disorder configurations chosen according to a binary distribution. Our numerical results show that the critical properties of the model are independent of q in agreement with a renormalization group analysis of Senthil and Majumdar (Phys. Rev. Lett. 76, 3001 (1996)). We show how an accurate analysis of moments of the distribution of magnetizations allows a precise determination of critical exponents, circumventing some problems related to binary disorder. Multiscaling properties of the model and dynamical correlation functions are also investigated. 05.50.+q, 64.60.Fr

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Section: Introductionsupporting

confidence: 79%

Critical behavior of the random Potts chain

Carlon¹,

Chatelain²,

Berche³

1999

Phys. Rev. B

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“…For a description of the algorithm and details of the implementation we refer to. 14) First, we have checked our method for the pure case (i.e. p = 1), for which the phase diagram is already known and the critical field value and the thermal exponents have been estimated from series expansions.…”

Section: ) 4)mentioning

confidence: 99%

“…In the continuous time method, following Kawashima and Rieger,14) the expectation value for the local susceptibility is…”

Section: ) 4)mentioning

confidence: 99%

Griffiths-McCoy Singularities in the Transverse Field Ising Model on the Randomly Diluted Square Lattice

1998

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The site-diluted transverse field Ising model in two dimensions is studied with QuantumMonte-Carlo simulations. Its phase diagram is determined in the transverse field (Γ) and temperature (T ) plane for various (fixed) concentrations (p). The nature of the quantum Griffiths phase at zero temperature is investigated by calculating the distribution of the local zero-frequency susceptibility. It is pointed out that the nature of the Griffiths phase is different for small and large Γ.KEYWORDS: QPT; Griffiths-McCoy singularities; multi-critical point; dynamical exponent §1. IntroductionIn numerous investigations of the effect of quantum fluctuations on the order-disorder phase transition the transverse-field spin-1/2 Ising model with ferromagnetic interactions has served as the simplest model on which these effects can be studied. 1) This model is of particular interest, since the strength of the quantum fluctuations can be controlled by varying the strength Γ of the transverse field: a pure quantum phase transition (QPT) occurs at zero temperature when the external field exceeds a critical value. The necessary prerequisite for the existence of long range order is the existence of an infinite connected component or cluster in the lattice, because only an infinite system can have a spontaneous magnetization. As has been recognized by Harris in the context of randomly site diluted lattices an infinite connected cluster is not only necessary but also sufficient for the existence of such a QPT. Any percolating cluster is at least one-dimensional (i.e. the fractal dimension of its backbone is larger than one). Since even the one-dimensional transverse field Ising model shows a QPT at some non-vanishing strength of the transverse field, any infinite cluster must have a QPT.The investigation of the effects of randomness on the transverse field Ising models (TFI) has 1 attracted a lot of interest recently. 2) In particular, the peculiar features of random systems which derive from the Griffiths-McCoy singularity have been studied intensively. 3), 4)As Griffiths has pointed out, 3) randomly diluted (classical) ferromagnets have a non-analytic free energy even away from the thermodynamical critical temperature for a given concentration p.As a matter of fact for any fixed concentration p of occupied sites such a non-analytic behavior persists up to a temperature which coincides with the transition temperature of the pure case (T c for p = 1). The reason for these anomalies is that there is a non-vanishing probability to find arbitrarily large clusters of connected spins for any concentration p. Since large clusters tend to order ferromagnetically below T c , they act very coherently. This causes singularities in the response to an external field and in the dynamical properties even above the critical point. These effects have been pointed out as significant effects in the distribution of zeros of the partition function and the Laplace transform of dynamical correlation. 5)The Griffiths phase persists in the presence of a transv...

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“…For systems without quenched disorder these are important to understand phenomena such as coarsening and domain growth 3 . In systems such as spin glasses [4][5][6][7][8] , random fields, interfaces, glasses in vortex systems 12,15,13 , which are dominated by quenched disorder and ultra slow relaxations, a detailed understanding of out of equilibrium dynamics becomes absolutely necessary to make contact with numerical simulations and experiments. These usually involve studying relaxation dynamics from an initial configuration at t = 0 (e.g uncorrelated) and asking about correlations in the systems between two later times t ′ (also called t w the waiting time) and t < t ′ .…”

Section: Introductionmentioning

confidence: 99%

“…A stronger form of aging seems to be observed 4,5 , and was proposed for spin glasses where the linear response shows memory effects, e.g the remanent linear magnetization after applying a field during time t w decays very slowly over a time scale set only by t w . Other puzzling phenomena such as memory under thermal cycling are observed 4,6,7 . There is at present no theory which would account fully for all these phenomena 9 , and understanding is only partial.…”

Section: Introductionmentioning

confidence: 99%

Aging and diffusion in low dimensional environments

Laloux

Doussal

1998

Phys. Rev. E

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We study out of equilibrium dynamics and aging for a particle diffusing in one dimensional environments, such as the random force Sinai model, as a toy model for low dimensional systems. We study fluctuations of two times (tw, t) quantities from the probability distribution Q(z, t, tw) of the relative displacement z = x(t) − x(tw) in the limit of large waiting time tw → ∞ using numerical and analytical techniques. We find three generic large time regimes: (i) a quasi-equilibrium regime (finite τ = t − tw) where Q(z, τ ) satisfies a general FDT equation (ii) an asymptotic diffusion regime for large time separation whereIn the unbiased Sinai model we find numerical evidence for regime (i) and (ii), and for (iii) with Q(z, t, t ′ ) = Q0(z)f (h(t)/h(t ′ )) and h(t) ∼ ln t. Since h(t) ∼ L(t) in Sinai's model there is a singularity in the diffusion regime to allow for regime (iii). A directed model, related to the biased Sinai model is solved and shows (ii) and (iii) with strong non self-averaging properties. Similarities and differences with mean field results are discussed. A general approach using scaling of next highest encountered barriers is proposed to predict aging properties, h(t) and f (x) in landscapes with fast growing barriers. It accounts qualitatively for aging in Sinai's model. We also identify a mecanism for aging in low dimensional phase space corresponding to an almost degeneracy of barriers. We illustrate this mechanism by introducing a new exactly solvable model, with barriers and wells, which shows clearly diffusion and aging regimes with a rich variety of functions h(t).

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Resistance Training for Special Populations

Cited by 7 publications

References 0 publications

Critical behavior of the random Potts chain

Critical behavior of the random Potts chain

Griffiths-McCoy Singularities in the Transverse Field Ising Model on the Randomly Diluted Square Lattice

Aging and diffusion in low dimensional environments

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