Lower and upper bounds on the fidelity susceptibility

We derive upper and lower bounds on the fidelity susceptibility in terms of macroscopic thermodynamical quantities, like susceptibilities and thermal average values. The quality of the bounds is checked by the exact expressions for a single spin in an external magnetic field. Their usefulness is illustrated by two examples of many-particle models which are exactly solved in the thermodynamic limit: the Dicke superradiance model and the single impurity Kondo model. It is shown that as far as divergent behavior is considered, the fidelity susceptibility and the thermodynamic susceptibility are equivalent for a large class of models exhibiting critical behavior.Comment: 19 page

Exact results for some Madelung type constants in the finite-size scaling theory

A general formula is obtained from which the madelung type constant: $$C(d|\nu)=\int_0^\infty dx x^{d/2-\nu-1}[(\sum_{l=-\infty}^\infty e^{-xl^2})^d-1-(\frac\pi x)^{d/2}]$$ extensively used in the finite-size scaling theory is computed analytically for some particular cases of the parameters $d$ and $\nu$. By adjusting these parameters one can obtain different physical situations corresponding to different geometries and magnitudes of the interparticle interaction.Comment: IOP- macros, 5 pages, replaced with amended version (1 ref. added

Exact solution of the anisotropic special transition in the O(n) model in 2D

The effect of surface exchange anisotropies is known to play a important role in magnetic critical and multicritical behavior at surfaces. We give an exact analysis of this problem in d=2 for the O(n) model by using Coulomb gas, conformal invariance and integrability techniques. We obtain the full set of critical exponents at the anisotropic special transition--where the symmetry on the boundary is broken down to O(n_1)xO(n-n_1)--as a function of n_1. We also obtain the full phase diagram and crossover exponents. Crucial in this analysis is a new solution of the boundary Yang-Baxter equations for loop models. The appearance of the generalization of Schramm-Loewner Evolution SLE_{\kappa,\rho} is also discussed.Comment: 4 pages, 2 figure

Generalized Casimir forces in non-equilibrium systems

In the present work we propose a method to determine fluctuation induced forces in non equilibrium systems. These forces are the analogue of the well known Casimir forces, which were originally introduced in Quantum Field theory and later extended to the area of Critical Phenomena. The procedure starts from the observation that many non equilibrium systems exhibit long-range correlations and the associated structure factors diverge in the long wavelength limit. The introduction of external bodies into such systems in general modifies the spectrum of these fluctuations and leads to the appearance of a net force between these bodies. The mechanism is illustrated by means of a simple example: a reaction diffusion equation with random noises.Comment: Submitted to Europhysics Letters. 7 pages, 2 figure

Integrals of Motion for Critical Dense Polymers and Symplectic Fermions

We consider critical dense polymers ${\cal L}(1,2)$. We obtain for this model the eigenvalues of the local integrals of motion of the underlying Conformal Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed description of the relation between this model and Symplectic Fermions including the indecomposable structure of the transfer matrix. Integrals of motion are defined directly on the lattice in terms of the Temperley Lieb Algebra and their eigenvalues are obtained and expressed as an infinite sum of the eigenvalues of the continuum integrals of motion. An elegant decomposition of the transfer matrix in terms of a finite number of lattice integrals of motion is obtained thus providing a reason for their introduction.Comment: 53 pages, version accepted for publishing on JSTA

Layer Features of the Lattice Gas Model for Self-Organized Criticality

A layer-by-layer description of the asymmetric lattice gas model for 1/f-noise suggested by Jensen [Phys. Rev. Lett. 64, 3103 (1990)] is presented. The power spectra of the lattice layers in the direction perpendicular to the particle flux is studied in order to understand how the white noise at the input boundary evolves, on the average, into 1/f-noise for the system. The effects of high boundary drive and uniform driving force on the power spectrum of the total number of diffusing particles are considered. In the case of nearest-neighbor particle interactions, high statistics simulation results show that the power spectra of single lattice layers are characterized by different $\beta_x$ exponents such that $\beta_x \to 1.9$ as one approaches the outer boundary.Comment: LaTeX, figures upon reques

Casimir force in the rotor model with twisted boundary conditions

We investigate the three dimensional lattice XY model with nearest neighbor interaction. The vector order parameter of this system lies on the vertices of a cubic lattice, which is embedded in a system with a film geometry. The orientations of the vectors are fixed at the two opposite sides of the film. The angle between the vectors at the two boundaries is $\alpha$ where $0 \le \alpha \le \pi$. We make use of the mean field approximation to study the mean length and orientation of the vector order parameter throughout the film---and the Casimir force it generates---as a function of the temperature $T$, the angle $\alpha$, and the thickness $L$ of the system. Among the results of that calculation are a Casimir force that depends in a continuous way on both the parameter $\alpha$ and the temperature and that can be attractive or repulsive. In particular, by varying $\alpha$ and/or $T$ one controls \underline{both} the sign \underline{and} the magnitude of the Casimir force in a reversible way. Furthermore, for the case $\alpha=\pi$, we discover an additional phase transition occurring only in the finite system associated with the variation of the orientations of the vectors.Comment: 14 pages, 9 figure

The Kasteleyn model and a cellular automaton approach to traffic flow

We propose a bridge between the theory of exactly solvable models and the investigation of traffic flow. By choosing the activities in an apropriate way the dimer configurations of the Kasteleyn model on a hexagonal lattice can be interpreted as space-time trajectories of cars. This then allows for a calculation of the flow-density relationship (fundamental diagram). We further introduce a closely-related cellular automaton model. This model can be viewed as a variant of the Nagel-Schreckenberg model in which the cars do not have a velocity memory. It is also exactly solvable and the fundamental diagram is calculated.Comment: Latex, 13 pages including 3 ps-figure

Fisher's scaling relation above the upper critical dimension

Fisher's fluctuation-response relation is one of four famous scaling formulae and is consistent with a vanishing correlation-function anomalous dimension above the upper critical dimension d_c. However, it has long been known that numerical simulations deliver a negative value for the anomalous dimension there. Here, the apparent discrepancy is attributed to a distinction between the system-length and correlation- or characteristic-length scales. On the latter scale, the anomalous dimension indeed vanishes above d_c and Fisher's relation holds in its standard form. However, on the scale of the system length, the anomalous dimension is negative and Fisher's relation requires modification. Similar investigations at the upper critical dimension, where dangerous irrelevant variables become marginal, lead to an analogous pair of Fisher relations for logarithmic-correction exponents. Implications of a similar distinction between length scales in percolation theory above d_c and for the Ginzburg criterion are briefly discussed.Comment: Published version has 6 pages, 2 figure

On the finite-size behavior of systems with asymptotically large critical shift

Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature $T_c$ are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent $\lambda$ characterizing the shift of the finite-size critical temperature with respect to $T_c$ is smaller than $1/\nu$, with $\nu$ being the critical exponent of the bulk correlation length.Comment: 24 pages, late