Related papers: Optimal Cooperation and Submodularity for Computin…
We study the $q$ states Potts model with four site interaction on the square lattice. Based on the asymptotic behaviour of lattice animals, it is argued that when $q\leq 4$ the system exhibits a second-order phase transition, and when $q >…
Cooperative optimization is a new way for finding global optima of complicated functions of many variables. It has some important properties not possessed by any conventional optimization methods. It has been successfully applied in solving…
We consider an energy minimization problem for cooperative LTE networks. To reduce energy consumption, we investigate how to jointly optimize the transmit power and the association between cells and user equipments (UEs), by taking into…
The optimization of submodular functions on the integer lattice has received much attention recently, but the objective functions of many applications are non-submodular. We provide two approximation algorithms for maximizing a…
The distribution of the zeros of the partition function in the complex temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is studied for non-integer Q. On $L\times L$ self-dual lattices studied ($L\le8$), no Fisher…
We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex square-lattice strip graphs $G$ for a variety of transverse widths $L_t$ and for arbitrarily…
The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered.…
In my PhD thesis I studied cooperative phenomena arise in complex systems using the methods of statistical and computational physics. The aim of my work was also to study the critical behaviour of interacting many-body systems during their…
We propose an experimental setup of ultracold fermions in an optical lattice to determine the pairing gap in a superfluid state and the spin ordering in a Mott-insulating state. The idea is to apply a periodic modulation of the lattice…
We study the phase diagram of the ferromagnetic $q$-state Potts model on the various three-dimensional lattices for integer and non-integer values of $q>1$. Our approach is based on a thermodynamically self-consistent Ornstein-Zernike…
We present exact calculations of the $q$-state Potts model partition functions and the equivalent Tutte polynomials for chain graphs comprised of $m$ repeated hammock subgraphs $H_{e_1,...,e_r}$ connected with line graphs of length $e_g$…
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…
Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little…
It is shown that the canonical problem of classical statistical thermodynamics, the computation of the partition function, is in the case of +/-J Ising spin glasses a particular instance of certain simple sums known as quadratically signed…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
The zeros of the partition function of the ferromagnetic q-state Potts model with long-range interactions in the complex-q plane are studied in the mean-field case, while preliminary numerical results are reported for the finite 1d chains…
We study coupled quantum systems as the working media of thermodynamic machines. Under a suitable phase-space transformation, the coupled systems can be expressed as a composition of independent subsystems. We find that for the coupled…
Maximum quantum work extraction is generally defined in terms of the ergotropy functional, no matter how experimentally complicated is the implementation of the optimal unitary allowing for it, especially in the case of multipartite…
We present exact solutions for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial $P$) on tube sections of the simple cubic lattice of fixed transverse size $L_x \times…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…