Related papers: On the pair correlation function of the Sine$_\bet…
We prove an operator level limit for the circular Jacobi $\beta$-ensemble. As a result, we characterize the counting function of the limit point process via coupled systems of stochastic differential equations. We also show that the…
We derive and solve flow equations for a general O(N)-symmetric effective potential including wavefunction renormalization corrections combined with a heat-kernel regularization. We investigate the model at finite temperature and study the…
In this article, we prove some results concerning the truncated two-point function of the infinite-range Ising model above and below the critical temperature. More precisely, if the coupling constants are of the form $J_{x}= \psi(x)e^{…
We study the linear statistics of the circular $\beta$-ensemble with a Stein's method argument, where the exchangeable pair is generated through circular Dyson Brownian motion. This generalizes previous results obtained in such a way for…
Ageing in systems without detailed balance is studied in the exactly solvable bosonic contact process and the critical bosonic pair-contact process. The two-time correlation function and the two-time response function are explicitly found.…
In this paper we have presented the calculation of pair correlation functions in a nematic phase for a model of spherical particles with the long-range anisotropic interaction from the mean spherical approximation(MSA) and the Percus-Yevick…
The one-dimensional pair contact process with a particle source is studied by using dynamical cluster mean-field approximations with sites up to $n=12$. The results obtained for different levels of approximation become convergent especially…
In a celebrated paper, Dyson shows that the spectrum of an n\times n random Hermitian matrix, diffusing according to an Ornstein-Uhlenbeck process, evolves as n noncolliding Brownian motions held together by a drift term. The universal edge…
We develop a systematic perturbative expansion and compute the one-loop two-points, three-points and four-points correlation functions in a non-commutative version of the U(N) Wess-Zumino-Witten model in different regimes of the…
For general $\beta \geq 1$, we consider Dyson Brownian motion at equilibrium and prove convergence of the extremal particles to an ensemble of continuous sample paths in the limit $N \to \infty$. For each fixed time, this ensemble is…
Using the superspace formalism, we compute for the two-dimensional N=1 supersymmetric non-linear $\sigma$-model, the order $(\alpha^{\prime})^{2}$ $(R_{mnpq})^2$ (three-loop) correction to the central charge via the operator product…
The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables…
We have computed through order $\beta^{21}$ the high-temperature expansions for the nearest-neighbor spin correlation function $G(N,\beta)$ of the classical N-vector model, with general N, on the simple-cubic and on the body-centered-cubic…
A schematic study of the $\beta \beta 2\nu $-decay of $^{48}Ca$ is made in a shell-model approach. The emphasis is especially put on the role of the spin-orbit potential in relation with the contribution of other terms in the strong…
A coagulation process is studied in a set of random masses, in which two randomly chosen masses and the smallest mass of the set multiplied by some fixed parameter $\omega\in [-1,1]$ are iteratively added. Besides masses (or primary…
Correlation functions measured as a function of $\Delta \eta, \Delta \phi$ have emerged as a powerful tool to study the dynamics of particle production in nuclear collisions at high energy. They are however subject, like any other…
Using $U_q[SU(2)]$ tensor calculus we compute the two-point scalar operators (TPSO), their averages on the ground-state give the two-point correlation functions. The TPSOs are identified as elements of the Temperley-Lieb algebra and a…
The pair contact process with diffusion is studied by means of multispin Monte Carlo simulations and density matrix renormalization group calculations. Effective critical exponents are found to behave nonmonotonically as functions of time…
We consider general renormalizable scalar field theory and derive six-loop beta functions for all parameters in d = 4 dimensions within the $\overline{MS}$-scheme. We do not explicitly compute relevant loop integrals but utilize…
We study the correlation energy associated with the pair fluctuations in BCS theory. We use a schematic two-level pairing model and discuss the behavior of the correlation energy across shell closures, including the even-odd differences. It…