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 and duality in the Ashkin Teller model

We report on the numerical measures on different spin interfaces and FK cluster boundaries in the Askhin-Teller (AT) model. For a general point on the AT critical line, we find that the fractal dimension of a generic spin cluster interface can take one of four different possible values. In particular we found spin interfaces whose fractal dimension is d_f=3/2 all along the critical line. Further, the fractal dimension of the boundaries of FK clusters were found to satisfy all along the AT critical line a duality relation with the fractal dimension of their outer boundaries. This result provides a clear numerical evidence that such duality, which is well known in the case of the O(n) model, exists in a extended CFT.Comment: 5 pages, 4 figure

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

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

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

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