Related papers: Higher Derivative Sigma Models
With the maturation of differentiable physics, its role in various downstream applications: such as model predictive control, robotic design optimization, and neural PDE solvers, has become increasingly important. However, the derivative…
Model Hamiltonians with long-range interaction yield energies that are corrected taking into account the universal behavior of the electron-electron interaction at short range. Although the intention of the paper is to explore the…
For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential.…
Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…
We recently introduced a robust approach to the derivation of sharp asymptotic formula for correlation functions of statistical mechanics models in the high-temperature regime. We describe its application to the nonperturbative proof of…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
Physics simulation is ubiquitous in robotics. Whether in model-based approaches (e.g., trajectory optimization), or model-free algorithms (e.g., reinforcement learning), physics simulators are a central component of modern control pipelines…
We consider gauge coupling unification in Lee-Wick extensions of the Standard Model that include higher-derivative quadratic terms beyond the minimally required set. We determine how the beta functions are modified when some Standard Model…
Following recent work on GLSM localization, we work out curvature couplings for rigidly supersymmetric nonlinear sigma models with superpotential for general target spaces, describing both ordinary and twisted chiral superfields on round…
We propose to slightly generalize the DeWitt-Schwinger adiabatic renormalization subtractions in curved space to include an arbitrary renormalization mass scale $\mu$. The new predicted running for the gravitational couplings are fully…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…
This paper focuses on extending our previous discussion of an Abelian U(1) gauge theory involving infinite derivatives to a non-Abelian SU(N) case. The renormalization group equation (RGEs) of the SU(N) gauge coupling is calculated and…
We complete a program of study of SU(N) gauge theories coupled to two flavors of fermions in the two-index symmetric representation by performing numerical simulations in SU(4). The beta function, defined and calculated via the…
The renormalization procedure of the non-linear SU(2) sigma model in D=4 proposed in hep-th/0504023 and hep-th/0506220 is here tested in a truly non-trivial case where the non-linearity of the functional equation is crucial. The simplest…
The transport of magnetization is analyzed for the classical Heisenberg chain at and especially above the isotropic point. To this end, the Hamiltonian equations of motion are solved numerically for initial states realizing harmonic-like…
In the Standard Model, partial unification of the non-Abelian running gauge couplings is achieved at the scale $\mu^{SM}_{32} \approx 2.8 \times 10^{16}$ GeV. Elaborating on this fact, we discuss a simple general parametrization for the new…
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…
We have simulated the two-dimensional $RP^2$ and $RP^3$ $\sigma$-models, at correlation lengths up to about 220 (resp.\ 30), using a Wolff-type embedding algorithm. We see no evidence of asymptotic scaling. Indeed, the data rule out the…
We study analytically the performance of a recently proposed algorithm for learning the couplings of a random asymmetric kinetic Ising model from finite length trajectories of the spin dynamics. Our analysis shows the importance of the…