Related papers: High-low temperature dualities for the classical $…
We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling constants or temperatures. We are led to…
We give a review of the one-loop divergences in higher derivative gravity theories. We first make the bilinear expansion in the quantum fluctuation on arbitrary backgrounds, introduce a higher-derivative gauge fixing and show that…
For $\alpha\geq 0$, $\delta>0$, $\beta<1$ and $\gamma\geq 0$, the class $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ consist of analytic and normalized functions $f$ along with the condition \begin{align*} {\rm Re\,}…
Low-temperature magnetic properties of both classical and quantum dimerized ferromagnetic spin chains are studied. It is shown that at low temperatures the classical dimerized model reduces to the classical uniform model with the effective…
For $d\geq 1$ and $0<\beta<\alpha<2$, consider a family of pseudo differential operators $\{\Delta^{\alpha} + a^\beta \Delta^{\beta/2}; a \in [0, 1]\}$ that evolves continuously from $\Delta^{\alpha/2}$ to $ \Delta^{\alpha/2}+…
An expansion in the number of spatial covariant derivatives is carried out to compute the $\zeta$-function regularized effective action of 2+1-dimensional fermions at finite temperature in an arbitrary non-Abelian background. The real and…
We consider quantum corrections to classical real time correlation functions at finite temperature. We derive a semi-classical expansion in powers of $\hbar$ with coefficients including all orders in the coupling constant. We give explicit…
The running coupling of a generic field theory can be described through a separable differential equation involving the corresponding $\beta$-function. Only the first loop order can be solved analytically in terms of well-known functions,…
In this paper we commence the study of discrete harmonic analysis associated with Jacobi orthogonal polynomials of order $(\alpha,\beta)$. Particularly, we give the solution $W^{(\alpha,\beta)}_t$, $t\ge 0$, and some properties of the heat…
We give a first principles formulation of the equilibrium statistical mechanics of strings in the canonical ensemble, compatible with the Euclidean timelike T-duality transformations that link the six supersymmetric string theories in…
We calculate the far-from-equilibrium dynamics and thermalization both for the quantum and the classical O(N)--model. The early and late-time behavior can be described from the 2PI--loop expansion for weak couplings or the nonperturbative…
The aim of this paper is to identify the limit in a high temperature regime of classical beta ensembles on the real line and related eigenvalue processes by using the Markov--Krein transform. We show that the limiting measure of Gaussian…
The rigorous explanation for the term $| t |^{2\beta}$ in the rectilinear diameter equation is given ($t = (T_c-T)/T_c$, $\beta$ is the critical exponent for the asymptotic form of the equation of state). The optimal order parameter, for…
This paper examines the global regularity problem on the two-dimensional incompressible Boussinesq equations with fractional dissipation, given by $\Lambda^\alpha u$ in the velocity equation and by $\Lambda^\beta \theta$ in the temperature…
Effective critical exponents for the \lambda \phi^4 scalar field theory are calculated as a function of the renormalization group block size k_o^{-1} and inverse critical temperature \beta_c. Exact renormalization group equations are…
We apply the results recently derived by Rojas et al. to derive the beta-expansion of the Helmholtz free energy of the spin-1 XXZ Heisenberg model up to 5th order in beta. The analytical expansion obtained is valid for all phases of this…
The method which allows for asymptotic expansion of the one-loop effective action W=ln det A is formulated. The positively defined elliptic operator A= U + M^2 depends on the external classical fields taking values in the Lie algebra of the…
We calculate the high-temperature series of the magnetic susceptibility and the second and fourth moments of the correlation function for the XY model on the square lattice to order $\beta^{33}$ by applying the improved algorithm of the…
For $\beta<\frac13$, we consider $C^\beta(\mathbb{T}^3\times [0,T])$ weak solutions of the incompressible Euler equations that do not conserve the kinetic energy. We prove that for such solutions the closed and non-empty set of singular…
We propose a novel method for renormalization group improvement of thermally resummed effective potential. In our method, $\beta$-functions are temperature dependent as a consequence of the divergence structure in resummed perturbation…