Related papers: Disordered Field Theory in $d=0$ and Distributiona…
The Argand diagram is used to display some characteristics of the Riemann Zeta function. The zeros of the Zeta function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram.…
For the generalized Ising models with all possible interactions within a face of the square lattice the formulas for finding partition function and free energy per lattice site in the thermodynamic limit were derived on a certain, in the…
With the help of metadynamics it is possible to calculate efficiently the free energy of systems displaying high energy barriers as a function of few selected "collective variables". In doing this, the contribution of all the other degrees…
Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods.…
A method which uses a generalized tensorial $\zeta$-function to compute the renormalized stress tensor of a quantum field propagating in a (static) curved background is presented. The starting point of the method is the direct computation…
A Wright function based framework is proposed to combine and extend several distribution families. The $\alpha$-stable distribution is generalized by adding the degree of freedom parameter. The PDF of this two-sided super distribution…
We present a \emph{new} formulation of perturbation theory for quantum systems, designated here as: `mean field perturbation theory'(MFPT), which is free from power-series-expansion in any physical parameter, including the coupling…
Accurate and robust spatial orders are ubiquitous in living systems. In 1952, Alan Turing proposed an elegant mechanism for pattern formation based on spontaneous breaking of the spatial translational symmetry in the underlying…
With a large-scale integration of distributed energy resources (DERs), distribution systems are expected to be capable of providing capacity support for the transmission grid. To effectively harness the collective flexibility from massive…
We study a zero-temperature phase transition in the random field Ising model on scale-free networks with the degree exponent $\gamma$. Using an analytic mean-field theory, we find that the spins are always in the ordered phase for…
We investigate the low temperature behavior of a system in a spontaneously broken symmetry phase described by an Euclidean quantum $\lambda\varphi^{4}_{d+1}$ model with quenched disorder. Using a series representation for the averaged…
We present a theoretical first-principles method to calculate the free energy of a magnetic system in its high-temperature paramagnetic phase, including vibrational, electronic, and magnetic contributions. The method for calculating free…
The Casimir free energy for a system of two dielectric concentric nonmagnetic spherical bodies is calculated with use of a quantum statistical mechanical method, at arbitrary temperature. By means of this rather novel method, which turns…
The selfconsistent approach to the 2D Ising Model with quenched random bonds is extended to the full lattice theory of four real fermions. The additional degrees of freedom, neglected in the renormalization-group theory, lead to a new phase…
We construct the field theory which describes the universal properties of the quasi-static isotropic depinning transition for interfaces and elastic periodic systems at zero temperature, taking properly into account the non-analytic form of…
This paper extends the investigation of energy distribution in finite settings, which is related to the results established in [H]. We analyze the distribution of multiplicative energies using Fourier analytical methods and random…
A method to regularize and renormalize the fluctuations of a quantum field in a curved background in the $\zeta$-function approach is presented. The method produces finite quantities directly and finite scale-parametrized counterterms at…
The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived, using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related…
The problem of pseudo-gap formation in an electronic system, induced by the fluctuations of the order parameter is revisited. We make the observation that a large class of current theories are theoretically equivalent to averaging the Free…
Sigma models arise frequently in particle physics and condensed-matter physics as low-energy effective theories. In this paper I compute the exact free energy at any temperature in two hierarchies of integrable sigma models in two…