相关论文: The Phase Transition in Exact Cover

We prove that, with high probability, the contradictory components of a random 2-SAT formula in the subcritical phase of the phase transition have only 3-regular kernels. This follows from the relation between these kernels and the complex…

A discussion is presented on the crossover of the susceptibility from mean-field to Ising critical behavior upon approaching the critical point from below and from above Tc, both for He3 and Xe. Fits of the experimental susceptibility data…

It is well known that there is a sharp density threshold for a random $r$-SAT formula to be satisfiable, and a similar, smaller, threshold for it to be satisfied by the pure literal rule. Also, above the satisfiability threshold, where a…

In this paper we study a variation of the random $k$-SAT problem, called polarized random $k$-SAT. In this model there is a polarization parameter $p$, and in half of the clauses each variable occurs negated with probability $p$ and pure…

Recently, the separated fragment (SF) has been introduced and proved to be decidable. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. The known upper bound on the time…

The quantitative adiabatic condition (QAC), or quantitative condition, is a convenient (a priori) tool for estimating the adiabaticity of quantum evolutions. However, the range of the applicability of QAC is not well understood. It has been…

The structural phase transitions and computational complexity of random 3-SAT instances are traditionally described using thermodynamic analogies from statistical physics, such as Replica Symmetry Breaking and energy landscapes. While…

Consider a random $k$-CNF formula $F_{k}(n, rn)$ with $n$ variables and $rn$ clauses. For every truth assignment $\sigma\in \{0, 1\}^{n}$ and every clause $c=\ell_{1}\vee\cdots\vee\ell_{k}$, let $d=d(\sigma, c)$ be the number of satisfied…

Optimization problems such as the NP-complete 3-SAT provide an important benchmark for the difficult task of finding ground-states in strongly correlated many-body systems with rugged energy landscapes. The study of random 3-SAT problems as…

Evaluating conditional coverage remains one of the most persistent challenges in assessing the reliability of predictive systems. Although conformal methods can give guarantees on marginal coverage, no method can guarantee to produce sets…

Winding number transitions in the two dimensional softly broken O(3) nonlinear sigma model are studied at finite energy and temperature. New periodic instanton solutions which dominate the semiclassical transition amplitudes are found…

In the variational approach to statistical mechanics, equilibrium states are the rigorous analogues of thermodynamic phases; the question of which invariant measures can arise as equilibrium states is therefore the question of which phases…

We study the phase transition and critical phenomenon for the grand canonical $\Phi^3$ measure in two-dimensional Euclidean quantum field theory. The study of this measure was initiated by Jaffe, Bourgain, and Carlen--Fr\"ohlich--Lebowitz,…

We point out that EXP3 can be implemented in constant time per round, propose more practical algorithms, and analyze the trade-offs between the regret bounds and time complexities of these algorithms.

Towards better understanding of how to design efficient adiabatic quantum algorithms, we study how the adiabatic gap depends on the spectra of the initial and final Hamiltonians in a natural family of test-bed examples. We show that perhaps…

Over the past few years three dimensional Quantum Electrodynamics (QED$_3$) has attracted a lot of attention, because it may be an effective theory for the underdoped and non-superconducting region of the phase diagram of high $T_c$ cuprate…

We study the electroweak phase transition in the minimal extension of the Standard Model: an extra complex singlet with zero vacuum expectation value. The first-order phase transition is strengthened by the cubic term triggered in the…

The Boolean Satisfiability Problem is perhaps one of the most well-known problems in theoretical computer science. On the one hand, it is proven to be NP-complete, which means that it is generally considered hard to solve. On the other…

Motivated by recent measurements for several alkali-metal atoms and alkali-metal-like ions, we perform a detailed study of electric dipole (E1) transition amplitudes in K, Ca+, Rb, Sr+, Cs, Ba+, Fr, and Ra+, which are of interest for…

Random constraint satisfaction problems (CSPs) have been widely studied both in AI and complexity theory. Empirically and theoretically, many random CSPs have been shown to exhibit a phase transition. As the ratio of constraints to…