Related papers: The random cluster model and new summation and int…
The theoretical analysis of spectral clustering mainly focuses on consistency, while there is relatively little research on its generalization performance. In this paper, we study the excess risk bounds of the popular spectral clustering…
The chiral Potts model continues to pose particular challenges in statistical mechanics: it is ``exactly solvable'' in the sense that it satisfies the Yang-Baxter relation, but actually obtaining the solution is not easy. Its free energy…
We show that the energy gap for the BCS gap equation is $ \Xi = \mu \left( 8 e^{-2} + o(1)\right) \exp\left( \frac{\pi}{2\sqrt{\mu} a}\right) $ in the low density limit $\mu \to 0$. Together with the similar result for the critical…
We perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states $Q\in (0,4)$ that are not necessarily integer. We compare these connectivities to four-point functions in a CFT…
We study the effect of varying strength, $\delta$, of bond randomness on the phase transition of the three-dimensional Potts model for large $q$. The cooperative behavior of the system is determined by large correlated domains in which the…
The statistics of the energy eigenvalues at the metal-insulator-transition of a two-dimensional disordered system with spin-orbit interaction is investigated numerically. The critical exponent $\nu$ is obtained from the finite-size scaling…
The XXX Heisenberg model is studied at finite temperature. The free energy is derived without recourse to Thermal Bethe Ansatz method and Quantum Transfer Matrix method. The result perfectly agrees with the free energy derived by Thermal…
In this paper we lay special stress on analyzing the topological properties of the lattice systems and try to ovoid the conventional ways to calculate the critical points. Only those clusters with finite sizes can execute the self similar…
We show that one can use some renormalized coupling constants to compute the free energy and correlation functions at all critical points of the two-dimensional topological gravity in a uniform way. In particular, one can derive the…
I formulate a class of relativistic quantum mechanical models that satisfy the cluster property and allow particle production. The models have a finite number of bare-particle degrees of freedom. The class of models include relativistic…
We study the random connection model on hyperbolic space $\mathbb{H}^d$ in dimension $d=2,3$. Vertices of the spatial random graph are given as a Poisson point process with intensity $\lambda>0$. Upon variation of $\lambda$ there is a…
An expansion of energy characteristics of wide thin slab of thickness L in power of 1/L is constructed using the free-electron approximation and the model of a potential well of finite depth. Accuracy of results in each order of the…
Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the…
Higher-order vertices at zero external momenta for the scalar field theory describing the critical behaviour of the Ising model are studied within the field-theoretical renormalization group (RG) approach in three dimensions. Dimensionless…
Entropy accumulation near a quantum critical point was expected based on general scaling arguments, and has recently been explicitly observed. We explore this issue further in two canonical models for quantum criticality, with particular…
In recent years, a better understanding of the Monte Carlo method has provided us with many new techniques in different areas of statistical physics. Of particular interest are so called cluster methods, which exploit the considerable…
We study a natural model of random 2-dimensional cubical complex which is a subcomplex of an n-dimensional cube, and where every possible square $2$-face is included independently with probability p. Our main result is to exhibit a sharp…
The random networks enriched with additional structures as metric and group-symmetry in background metric space are investigated. The important quantities like he clustering coefficient as well as the mean degree of separation in such…
The alternating integrable spin chain and the $RSOS(q_{1},q_{2};p)$ model in the presence of a quantum impurity are investigated. The boundary free energy due to the impurity is derived, the ratios of the corresponding $g$ functions at low…
The end-to-end energy - energy correlations of random transverse-field quantum Ising spin chains are computed using a generalization of an asymptotically exact real-space renormalization group introduced previously. Away from the critical…