711 research outputs found
Further evidence of the absence of Replica Symmetry Breaking in Random Bond Potts Models
In this short note, we present supporting evidence for the replica symmetric
approach to the random bond q-state Potts models. The evidence is statistically
strong enough to reject the applicability of the Parisi replica symmetry
breaking scheme to this class of models. The test we use is a generalization of
one formerly proposed by Dotsenko et al. and consists in measuring scaling laws
of disordered-averaged moments of the spin-spin correlation functions.
Numerical results, obtained via Monte Carlo simulations for several values of
q, are shown to be in fair agreement with the replica symmetric values computed
by using perturbative CFT for the second and third moments of the q=3 model.
RSB effects, which should increase in strength with moment, are unobserved.Comment: 7 pages, some minor modifications (mainly misprints). To Appear in
Europhysics Letter
Multicritical points for the spin glass models on hierarchical lattices
The locations of multicritical points on many hierarchical lattices are
numerically investigated by the renormalization group analysis. The results are
compared with an analytical conjecture derived by using the duality, the gauge
symmetry and the replica method. We find that the conjecture does not give the
exact answer but leads to locations slightly away from the numerically reliable
data. We propose an improved conjecture to give more precise predictions of the
multicritical points than the conventional one. This improvement is inspired by
a new point of view coming from renormalization group and succeeds in deriving
very consistent answers with many numerical data.Comment: 11 pages, 9 figures, 7 tables This is the published versio
Critical interfaces of the Ashkin-Teller model at the parafermionic point
We present an extensive study of interfaces defined in the Z_4 spin lattice
representation of the Ashkin-Teller (AT) model. In particular, we numerically
compute the fractal dimensions of boundary and bulk interfaces at the
Fateev-Zamolodchikov point. This point is a special point on the self-dual
critical line of the AT model and it is described in the continuum limit by the
Z_4 parafermionic theory. Extending on previous analytical and numerical
studies [10,12], we point out the existence of three different values of
fractal dimensions which characterize different kind of interfaces. We argue
that this result may be related to the classification of primary operators of
the parafermionic algebra. The scenario emerging from the studies presented
here is expected to unveil general aspects of geometrical objects of critical
AT model, and thus of c=1 critical theories in general.Comment: 15 pages, 3 figure
Identifying Heating Technologies suitable for Historic Churches, Taking into Account Heating Strategy and Conservation through Pairwise Analysis
As a result of difficulty meeting energy efficiency through fabric alteration, historic churches must focus on heating systems and operational strategy as key to reducing carbon emissions. Strategies can be defined as local or central heating. Local heating strives to heat occupants, while central heating aims to heat the building fabric and therefore the occupants. Each strategy requires a different approach to control and technology in response to priorities such as conservation, comfort and cost. This paper reviews current and emerging technologies in the context of church heating. The fuel source, heat generation technology and heat emitter are arranged in a matrix, with pairwise analysis undertaken to create weightings for each assessment criteria. The process of constructing the matrix and undertaking pairwise analysis using personas is discussed. The result is a ranking of fuels and technologies appropriate to the main priorities and individual preferences. Some desirable technologies are inherently more damaging to historic church environments due to invasive installation. These technologies score poorly when the aim is fabric preservation. Greener fuels, like biomass, may rank lower than fossil fuels, due in part to operational differences
Scale Invariance and Self-averaging in disordered systems
In a previous paper we found that in the random field Ising model at zero
temperature in three dimensions the correlation length is not self-averaging
near the critical point and that the violation of self-averaging is maximal.
This is due to the formation of bound states in the underlying field theory. We
present a similar study for the case of disordered Potts and Ising ferromagnets
in two dimensions near the critical temperature. In the random Potts model the
correlation length is not self-averaging near the critical temperature but the
violation of self-averaging is weaker than in the random field case. In the
random Ising model we find still weaker violations of self-averaging and we
cannot rule out the possibility of the restoration of self-averaging in the
infinite volume limit.Comment: 7 pages, 4 ps figure
Replica symmetry breaking transition of the weakly anisotropic Heisenberg spin glass in magnetic fields
The spin and the chirality orderings of the three-dimensional Heisenberg spin
glass with the weak random anisotropy are studied under applied magnetic fields
by equilibrium Monte Carlo simulations. A replica symmetry breaking transition
occurs in the chiral sector accompanied by the simultaneous spin-glass order.
The ordering behavior differs significantly from that of the Ising SG, despite
the similarity in the global symmetry. Our observation is consistent with the
spin-chirality decoupling-recoupling scenario of a spin-glass transition.Comment: 4 pages, 4 figure
Temperature Chaos, Rejuvenation and Memory in Migdal-Kadanoff Spin Glasses
We use simulations within the Migdal-Kadanoff real space renormalization
approach to probe the scales relevant for rejuvenation and memory in spin
glasses. One of the central questions concerns the role of temperature chaos.
First we investigate scaling laws of equilibrium temperature chaos, finding
super-exponential decay of correlations but no chaos for the total free energy.
Then we perform out of equilibrium simulations that follow experimental
protocols. We find that: (1) rejuvenation arises at a length scale smaller than
the ``overlap length'' l(T,T'); (2) memory survives even if equilibration goes
out to length scales much larger than l(T,T').Comment: 4 pages, 4 figures, added references, slightly changed content,
modified Fig.
Critical domain walls in the Ashkin-Teller model
We study the fractal properties of interfaces in the 2d Ashkin-Teller model.
The fractal dimension of the symmetric interfaces is calculated along the
critical line of the model in the interval between the Ising and the
four-states Potts models. Using Schramm's formula for crossing probabilities we
show that such interfaces can not be related to the simple SLE, except
for the Ising point. The same calculation on non-symmetric interfaces is
performed at the four-states Potts model: the fractal dimension is compatible
with the result coming from Schramm's formula, and we expect a simple
SLE in this case.Comment: Final version published in JSTAT. 13 pages, 5 figures. Substantial
changes in the data production, analysis and in the conclusions. Added a
section about the crossing probability. Typeset with 'iopart
Magnetic-glassy multicritical behavior of the three-dimensional +- J Ising model
We consider the three-dimensional model defined on a simple cubic
lattice and study its behavior close to the multicritical Nishimori point where
the paramagnetic-ferromagnetic, the paramagnetic-glassy, and the
ferromagnetic-glassy transition lines meet in the T-p phase diagram (p
characterizes the disorder distribution and gives the fraction of ferromagnetic
bonds). For this purpose we perform Monte Carlo simulations on cubic lattices
of size and a finite-size scaling analysis of the numerical results.
The magnetic-glassy multicritical point is found at , along the
Nishimori line given by . We determine the
renormalization-group dimensions of the operators that control the
renormalization-group flow close to the multicritical point, ,
, and the susceptibility exponent . The
temperature and crossover exponents are and , respectively. We also investigate the model-A dynamics, obtaining
the dynamic critical exponent .Comment: 17 page
- …