Hyperscaling violation in the 2D 8-state Potts model with long-range correlated disorder

The first-order phase transition of the two-dimensional eight-state Potts model is shown to be rounded when long-range correlated disorder is coupled to energy density. Critical exponents are estimated by means of large-scale Monte Carlo simulations. In contrast to uncorrelated disorder, a violation of the hyperscaling relation $\gamma/\nu=d-2x_\sigma$ is observed. Even though the system is not frustrated, disorder fluctuations are strong enough to cause this violation in the very same way as in the 3D random-field Ising model. In the thermal sector too, evidence is given for such violation in the two hyperscaling relations $\alpha/\nu=d-2x_\varepsilon$ and $1/\nu=d-x_\varepsilon$. In contrast to the random field Ising model, at least two hyperscaling violation exponents are needed. The scaling dimension of energy is conjectured to be $x_\varepsilon=a/2$, where $a$ is the exponent of the algebraic decay of disorder correlations.Comment: 6 pages, 6 figures. Published versio

Infinite disorder and correlation fixed point in the Potts model with correlated disorder

Recent Monte Carlo simulations of the q-state Potts model with a disorder displaying slowly-decaying correlations reported a violation of hyperscaling relation caused by large disorder fluctuations and the existence of a Griffiths phase, as in random systems governed by an infinite-disorder fixed point. New simulations, directly made in the limit of an infinite disorder strength, are presented. The magnetic scaling dimension is shown to correspond to the correlated percola-tion fixed point. The latter is shown to be unstable at finite disorder strength but with a large cross-over length which is not accessible to Monte Carlo simulations

Mark-up and Capital Structure of the Firm facing Uncertainty

This note shows that, with pre-set price and capital decisions of firms facing uncertainty and financial market imperfections, price, mark up and the expected degree of capacity utilization (resp. capital) decreases (resp. increases) with the firm internal net worth.capital, pricing, capital market imperfections

Diverging conductance at the contact between random and pure quantum XX spin chains

A model consisting in two quantum XX spin chains, one homogeneous and the second with random couplings drawn from a binary distribution, is considered. The two chains are coupled to two different non-local thermal baths and their dynamics is governed by a Lindblad equation. In the steady state, a current J is induced between the two chains by coupling them together by their edges and imposing different chemical potentials $\mu$ to the two baths. While a regime of linear characteristics J versus $\Delta$$\mu$ is observed in the absence of randomness, a gap opens as the disorder strength is increased. In the infinite-randomness limit, this behavior is related to the density of states of the localized states contributing to the current. The conductance is shown to diverge in this limit.Comment: 15 pages, 18 figure

Face-centred cubic lattices and particle redistribution in vortex methods

In vortex particle methods one is concerned with the problem of clustering and depletion of particles in different regions of the flow. The overlap of the vortex blobs is indeed of primary importance for the convergence of the method. In this paper we consider face-centred cubic (FCC) lattices for particle redistribution in three dimensions. This lattice is in fact the most natural way to pack spheres (the FCC is also known as a closest-sphere packing lattice). As a consequence, a point has 12 equidistant close neighbours rather than six for the cubic lattice. The FCC lattice thus offers some symmetry properties that should prove useful for a number of reasons, e.g., the core overlap issue. A few results for this scheme are presented. The problem of two colliding vortex rings at Re = 250 and 500 is studied with both the FCC and cubic lattice schemes. This problem subjects the vortex tubes to a quite strong stretching field and can amply test the quality of the lattice and the remeshing