相关论文: A generalized mean field theory of coarse-graining

Generic coarse-grained models are designed such that they are (i) simple and (ii) computationally efficient. They do not aim at representing particular materials, but classes of materials, hence they can offer insight into universal…

Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…

We study the dynamics and morphology of grain growth with anisotropic energy and mobility of grain boundaries using a generalized phase field model. In contrast to previous studies, both inclination and misorientation of the boundaries are…

Variational inference with a factorized Gaussian posterior estimate is a widely used approach for learning parameters and hidden variables. Empirically, a regularizing effect can be observed that is poorly understood. In this work, we show…

Generalized gauge fields are tensor fields with mixed symmetries. For gravity and higher spins in dimensions greater than four, the fundamental field in the "magnetic representation" is a generalized gauge field. It is shown that the analog…

The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…

In this paper, we explore the application of mean field theory, a technique from statistical physics, to deep metric learning and address the high training complexity commonly associated with conventional metric learning loss functions. By…

Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm \beta p^2$.…

After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…

We study the random-field Ising model with long-range interactions and show the exactness of the mean-field theory under certain mild conditions. This is a generalization of the result of Mori for the non-random and spin-glass cases. To…

Detailed mean field and Monte Carlo studies of the dynamic magnetization-reversal transition in the Ising model in its ordered phase under a competing external magnetic field of finite duration have been presented here. Approximate…

We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…

Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. We demonstrate how the long-ranged interactions responsible for this behavior arise naturally upon integrating out mechanical…

Mean-field models approximate large stochastic systems by simpler differential equations that are supposed to approximate the mean of the larger system. It is generally assumed that as the stochastic systems get larger (i.e., more people or…

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes…

We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…

Continuing earlier work, we apply the mean field method to the world sheet representation of a simple field theory. In particular, we study the higher order terms in the mean field expansion, and show that their cutoff dependence can be…

We describe a mean field technique for quantum string (or dimer) models. Unlike traditional mean field approaches, the method is general enough to include string condensed phases in addition to the usual symmetry breaking phases. Thus, it…

Coarse-graining has become an area of tremendous importance within many different research fields. For molecular simulation, coarse-graining bears the promise of finding simplified models such that long-time simulations of large-scale…

We derive mean-field equations for a general class of ferromagnetic spin systems with an explicit error bound in finite volumes. The proof is based on a link between the mean-field equation and the free convolution formalism of random…