Abstract Independent samples from the Boltzmann distribution are valuable for estimating spin-glass observables and evaluating approximate sampling methods. Local Markov chain Monte Carlo methods typically generate temporally correlated samples and can encounter critical slowing down or metastable trapping, while neural autoregressive samplers such as variational autoregressive networks generate independent but approximate samples. Here we present an exact autoregressive sampling algorithm for planar Ising spin glasses based on the Kac--Ward theory. Under the chain-rule factorization, sequentially fixing spins induces boundary-localized external fields, which destroy the zero-field structure required for exact evaluation. By encoding these fields with a planarity-preserving auxiliary spin construction, the conditional partition functions are mapped to an extended zero-field Ising model and exactly evaluated using the Kac--Ward determinant formula. The method generates strictly independent and identically distributed samples with exact normalized likelihoods at a computational cost of $\mathcal{O}(N^{5/2})$ for $N$ spins, thereby providing an exact baseline for benchmarking neural autoregressive samplers.
Abstract The dynamic magnetic properties and magnetocaloric effect of a sandwiched graphene‑fullerene composite are studied via Monte Carlo simulations of a mixed‑spin (1, 5/2) Ising model. The crystal field Db dominates the response, while increasing its strength lowers the phase transition temperature, enhances the entropy change, and shifts it to lower temperatures. Stronger exchange couplings Jab and Jb raise the transition temperature but reduce the entropy change, revealing a trade‑off. The amplitude of the oscillating field h0 dramatically increases the entropy change at the cost of narrowing the temperature range. The bias field hb stabilizes ferromagnetic order, while the period τ has a weaker effect. The relative cooling power is optimized at moderate crystal field, weak couplings, and optimal amplitude. This system is promising for Magnetocaloric effect.
Abstract We investigate nonsequential double ionization(NSDI) of Ar in cross-linearly-polarized two-color (CTC) laser fields, consisting of an 800-nm and a 400-nm field using a three-dimensional classical model. As the crossing angle of the CTC field increases, the NSDI yield exhibits a decrease followed by an increase. Back analysis reveals that the exit collision channel dominates at small angles while the recollision ionization channel dominates at large angles, leading to this nonmonotonic yield trend. The photoelectron momentum distributions (PEMDs) also exhibit the characteristic features of the respective channels at different angles. This indicates that by varying the crossing angle of the CTC field, NSDI can predominantly occur in a single ionization channel. Our results providing a new approach for controlling the correlated electron dynamics.
Abstract The structure-scalar formulation for hyperbolically symmetric fluids \cite{herrera2021hyperbolically} is generalized to the closed radial stability problem within general relativity. We keep the inner boundary condition on the mass function and find the linear metric constraints, density variation and oscillation operators for a particular Lagrangian pressure dependence and fixed anisotropy. The exact zero-complexity configuration, trapped between rigid boundaries, becomes an inverse-square spectral problem. Applying the logarithmic variable change results in a necessary and sufficient condition on the sign of the principal eigenvalue, a precise estimate of the number of unstable radial modes, and an analytic expression for marginal eigenfunctions. The stability diagram depends on the response coefficient and the annulus thickness, independent shooting and grid refinement verify the numerical spectrum. We also calculate the first-order complexity response and apply the variational method to a separate spherical constant-density reference star scaled to published NICER mass and radius values for PSR J0030+0451. A fixed-density mass--radius family also permits a high-mass comparison. This stellar calculation is illustrative rather than an observational fit and the hyperbolic result applies to the confined fluid sector. The principal contribution is an exact and reproducible constitutive stability diagram that adds dynamical information to Herrera's hyperbolic equilibrium framework.
Based on a coupled resonator array, we theoretically construct and numerically simulate a nonlinear quantum optics platform to dynamically control the Bloch wavevector. By scanning the modulation parameters ( alpha,ky), we reproduce the Hofstadter's butterfly structure in the biphoton energy spectrum and reveal clear correspondences among the eigenenergy spectrum, transmission spectrum, and biphoton joint spectral intensity (JSI). Further research demonstrates that screening the pump wavelength can effectively tailor the JSI profile and the Schmidt number of the quantum state, enabling flexible manipulation of frequency entanglement characteristics. This work provides a theoretical framework for exploring quantum state generation and manipulation in nonlinear topological photonic systems and demonstrates the potential for realizing programmable quantum light sources in integrated quantum photonic circuits.
