相关论文: Concurrence of Symmetry Breaking and Nonlocality P…

We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…

These notes are devoted to the statistical mechanics of directed polymers interacting with one-dimensional spatial defects. We are interested in particular in the situation where frozen disorder is present. These polymer models undergo a…

Spontaneous symmetry breaking is a well-understood mechanism for generating distinct phases of matter. Recently, the notion of symmetry has been broadened to include operations without inverses, leading to the concept of non-invertible…

The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified…

We show a dissipative phase transition in a driven nonlinear quantum oscillator in which a discrete time-translation symmetry is spontaneously broken in two different ways. The corresponding regimes display either discrete or incommensurate…

We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions…

A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…

We identify a new universality class of phase transitions that emerges in non-normal systems, extending the classical framework beyond eigenvalue instabilities. Unlike traditional critical phenomena, where transitions occur when eigenvalues…

Many physical systems, including classical fluids, present in their phase diagram the competition between two phases that are separated by a line of first-order phase transitions which terminates at a so-called critical point. Despite…

We propose a spreading model in multilayer networks and study the nature of nonequilibrium phase transition in the model. The model integrates the susceptible-infected-susceptible (or susceptible-infected-recovered) spreading dynamics with…

When a second-order phase transition is crossed at fine rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial…

A fast method is presented for simulating the dielectric-breakdown model using iterated conformal mappings. Numerical results for the dimension and for corrections to scaling are in good agreement with the recent RG prediction of an upper…

We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics…

Diffusion models, emerging as powerful deep generative tools, excel in various applications. They operate through a two-steps process: introducing noise into training samples and then employing a model to convert random noise into new…

Causality -- referring to temporal, uni-directional cause-effect relationships between components -- underlies many complex generative processes, including videos, language, and robot trajectories. Current causal diffusion models entangle…

Spatiotemporal image generation is a highly meaningful task, which can generate future scenes conditioned on given observations. However, existing change generation methods can only handle event-driven changes (e.g., new buildings) and fail…

Diffusion-based Deep Generative Models (DDGMs) offer state-of-the-art performance in generative modeling. Their main strength comes from their unique setup in which a model (the backward diffusion process) is trained to reverse the forward…

We study a zero-range process where the jump rates do not only depend on the local particle configuration, but also on the size of the system. Rigorous results on the equivalence of ensembles are presented, characterizing the occurrence of…

In this paper we analyse a class of nonlinear cross-diffusion systems for two species with local repulsive interactions that exhibit a formal gradient flow structure with respect to the Wasserstein metric. We show that systems where the…

Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…