相关论文: Tensor Network Finite-Size Scaling for Two-Dimensi…

A systematic method for the computation of finite temperature ($T$) crossover functions near quantum critical points close to, or above, their upper-critical dimension is devised. We describe the physics of the various regions in the $T$…

Energy eigenvalues and order parameters are calculated by exact diagonalization for the transverse Ising model on square lattices of up to 6x6 sites. Finite-size scaling is used to estimate the critical parameters of the model, confirming…

We perform high-statistics Monte Carlo simulations of three three-dimensional Ising spin-glass models: the +-J Ising model for two values of the disorder parameter p, p=1/2 and p=0.7, and the bond-diluted +-J model for bond-occupation…

Tensor networks such as matrix product states (MPS) and projected entangled pair states (PEPS) are commonly used to approximate quantum systems. These networks are optimized in methods such as DMRG or evolved by local operators. We provide…

In a number of classical statistical-physical models, there exists a characteristic dimensionality called the upper critical dimension above which one observes the mean-field critical behavior. Instead of constructing high-dimensional…

Transformer has been widely-used in many Natural Language Processing (NLP) tasks and the scaled dot-product attention between tokens is a core module of Transformer. This attention is a token-wise design and its complexity is quadratic to…

We study the critical dynamics of hyper-cubic finite size system in the presence of quenched short-range correlated disorder. By using the random $T_c$ model A for the critical dynamics and the renormalization group method in the vicinity…

The critical behavior of the two-dimensional XY model has been explored in the literature using various methods. They include the high-temperature expansion (HTE) method, Monte Carlo (MC) approach, strong coupling expansion method, and…

A nearest neighbour spin pair of the quasi-two-dimensional three-state Potts model interacts with the strength $J(>0)$ in the $xy$-plane and with $\lambda J$ $(0\le \lambda \ll 1)$ in the $z$-axis. The phase transition is of second-order…

Recently gigantic peaks in thermodynamic response functions have been observed at finite temperature for one-dimensional models with short-range coupling, closely resembling a second-order phase transition. Thus, we will analyze the finite…

We make a detailed analysis of the spontaneous $Z_{2}$-symmetry breaking in the two dimensional real $\phi^{4}$ theory with the tensor renormalization group approach, which allows us to take the thermodynamic limit easily and determine the…

We study a generalized clock model on the simple cubic lattice. The parameter of the model can be tuned such that the amplitude of the leading correction to scaling vanishes. In the main part of the study we simulate the model with $Z_8$…

Despite significant research on the optimization aspects of federated learning, the exploration of generalization error, especially in the realm of heterogeneous federated learning, remains an area that has been insufficiently investigated,…

Numerical studies of the Anderson transition are based on the finite-size scaling analysis of the smallest positive Lyapunov exponent. We prove numerically that the same scaling holds also for higher Lyapunov exponents. This scaling…

Recently developed tensor network methods demonstrate great potential for addressing the quantum many-body problem, by constructing variational spaces with polynomially, instead of exponentially, scaled parameters. Constructing such an…

The phase diagram of QCD at finite temperature and density and the existence of a critical point are currently very actively researched topics. Although tremendous progress has been made, in the case of two light quark flavors even the…

Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…

Numerical annealing and renormalization group have conceived various successful approaches to study the thermodynamics of strongly-correlated systems where perturbation or expansion theories fail to work. As the process of lowering the…

Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…

Colored tensor models generalize matrix models in arbitrary dimensions yielding a statistical theory of random higher dimensional topological spaces. They admit a 1/N expansion dominated by graphs of spherical topology. The simplest tensor…