Related papers: Replica method and finite volume corrections
Coupled cluster theory is one of the most popular post-Hartree-Fock methods for ab initio molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating…
We describe and analyze a computionally efficient refitting procedure for computing high-probability upper bounds on the instance-wise mean-squared prediction error of penalized nonparametric estimates based on least-squares minimization.…
We consider a recently proposed convex formulation, known as the PhaseMax method, for solving the phase retrieval problem. Using the replica method from statistical mechanics, we analyze the performance of PhaseMax in the high-dimensional…
The standard definition of particle number fluctuations based on point-like particles neglects the excluded volume effect. This leads to a large and systematic finite-size scaling and an unphysical surface term in the isothermal…
We show that theory predictions for volume reflection in bent crystals agree with recent experimental data. This makes possible to predict volume reflection angle and efficiency in a broad range of energy for various crystals. A simple…
Using the replica approach and the cavity method, we study the fluctuations of the optimal cost in the random-link matching problem. By means of replica arguments, we derive the exact expression of its variance. Moreover, we study the large…
Finite-size (FS) effects are a major source of error in many-body (MB) electronic structure calculations of extended systems. A method is presented to correct for such errors. We show that MB FS effects can be effectively included in a…
We analytically derive, in the context of the replica formalism, the first finite size corrections to the average optimal cost in the random assignment problem for a quite generic distribution law for the costs. We show that, when moving…
A unified formulation of one-loop tensor integrals is proposed for systematical calculations of finite volume corrections. It is shown that decomposition of the one-loop tensor integrals into a series of tensors accompanied by tensor…
Inspired by the recent development on calculating the free energy change via a relaxation process [Nat. Phys. 14, 842 (2018)], we investigate the role of heat released in an irreversible relaxation following a large perturbation. Utilizing…
Quantitative evaluations of the free energy of materials must take into account thermal and zero-point energy fluctuations. While these effects can easily be estimated within a harmonic approximation, corrections arising from the anharmonic…
Finite size effects for the Ising Model coupled to two dimensional random surfaces are studied by exploiting the exact results from the 2-matrix models. The fixed area partition function is numerically calculated with arbitrary precision by…
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the replica Z_n symmetry. It…
We present new error estimates for the finite volume and finite difference methods applied to the compressible Navier-Stokes equations. The main innovative ingredients of the improved error estimates are a refined consistency analysis…
We discuss finite-size effects in one disordered ${\lambda}{\phi}^{4}$ model defined in a $d$-dimensional Euclidean space. We consider that the scalar field satisfies periodic boundary conditions in one dimension and it is coupled with a…
Our previously-developed calculational method (the partial wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge fields. Our method proves to be…
We have studied the grand potential and phase transitions of an inhomogeneous finite volume spherical quark system. First the finite volume effects are considered by applying the multiple reflection expansion method which is an…
We describe a novel framework for partially quenched chiral perturbation theory based on the replica method. The computational rules are exceedingly simple. We illustrate these rules by computing the partially quenched chiral condensate to…
We discuss the finite volume corrections to fK and BK by using the one-loop chiral perturbation theory in full, quenched, and partially quenched QCD. We show that the finite volume corrections to these quantities dominate the physical…
Lattice regularization is used to perform chiral perturbation theory calculations in finite volume. The lattice spacing is chosen small enough to be irrelevant, and numerical results are obtained from simple summations.