Related papers: Computational Study of a Multistep Height Model
We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This…
The partition function of the O(n) loop model on the honeycomb lattice is mapped to that of the O(n) loop model on the 3-12 lattice. Both models share the same operator content and thus critical exponents. The critical points are related…
Variational algorithms have gained prominence over the past two decades as a scalable computational environment for Bayesian inference. In this article, we explore tools from the dynamical systems literature to study convergence of…
Experimental systems with a first order phase transition will often exhibit hysteresis when out of equilibrium. If defects are present, the hysteresis loop can have different shapes: with small disorder the hysteresis loop has a macroscopic…
A new graphical method is developed to calculate the critical temperature of 2- and 3-dimensional Ising models as well as that of the 2-dimensional Potts models. This method is based on the transfer matrix method and using the limited…
We apply a worm algorithm to simulate the quantum transverse-field Ising model in a path-integral representation of which the expansion basis is taken as the spin component along the external-field direction. In such a representation, a…
Stochastic point processes with Coulomb interactions arise in various natural examples of statistical mechanics, random matrices and optimization problems. Often such systems due to their natural repulsion exhibit remarkable hyperuniformity…
Surface hopping algorithms, as an important class of quantum dynamics simulation algorithms for non-adiabatic dynamics, are typically performed in the adiabatic representation, which can break down in the presence of ill-defined adiabatic…
The equilibrium ensemble approach to disordered systems is used to investigate the critical behaviour of the two dimensional Ising model in presence of quenched random site dilution. The numerical transfer matrix technique in semi- infinite…
We develop a method to improve on the statistical errors for higher moments using machine learning techniques. We present here results for the dual representation of the Ising model with an external field, derived via the high temperature…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
In critical lattice models, distance ($r$) dependent correlation functions contain power laws $r^{-2\Delta}$ governed by scaling dimensions $\Delta$ of an underlying continuum field theory. In Monte Carlo simulations, the leading dimensions…
We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\lambda$, in a scaling…
We study numerically the region above the critical temperature of the four dimensional Random Field Ising Model. Using a cluster dynamic we measure the connected and disconnected magnetic susceptibility and the connected and disconnected…
We rederive the finite size scaling formula for the apparent critical temperature by using Mean Field Theory for the Ising Model above the upper critical dimension. We have also performed numerical simulations in five dimensions and our…
Accurate numerical results are presented for the three-dimensional equivalent-neighbor model on a cubic lattice, for twelve different interaction ranges (coordination number between 18 and 250). These results allow the determination of the…
This study presents an enhanced theoretical formulation for bipedal hierarchical control frameworks under uneven terrain conditions. Specifically, owing to the inherent limitations of the Linear Inverted Pendulum Model (LIPM) in handling…
We apply a new updating algorithm scheme to investigate the critical behavior of the two-dimensional ferromagnetic Ising model on a triangular lattice with nearest neighbour interactions. The transition is examined by generating accurate…
Quantitative assessment of the growth of biological organisms has produced many mathematical equations. Many efforts have been given on statistical identification of the correct growth model from experimental data. Every growth equation is…
For multi-limbed robots, motion planning with posture and force constraints tends to be a difficult optimization problem due to nonlinearities, which also present extended solve times. We propose a multi-stage optimization framework with…