Evolution of Concentration Under Lattice Spin-Flip Dynamics

We consider spin-flip dynamics of Ising lattice spin systems and study the time evolution of concentration inequalities. For “weakly interacting” dynamics we show that the Gaussian concentration bound is conserved in the course of time and it is satisfied by the unique stationary Gibbs measure. Next we show that, for a general class of translation-invariant spin-flip dynamics, it is impossible to evolve in finite time from a low-temperature Gibbs state towards a measure satisfying the Gaussian concentration bound. Finally, we consider the time evolution of the weaker uniform variance bound, and show that this bound is conserved under a general class of spin-flip dynamics.

More exotic field theories in 3+1 dimensions

We continue the exploration of nonstandard continuum field theories related to fractons in 3+1 dimensions. Our theories exhibit exotic global and gauge symmetries, defects with restricted mobility, and interesting dualities. Depending on the model, the defects are the probe limits of either fractonic particles, strings, or strips. One of our models is the continuum limit of the plaquette Ising lattice model, which features an important role in the construction of the X-cube model.

ISING MODEL SIMULATIONS AS A TESTBED OF NUCLEATION THEORY

In this short review article we discuss the use of Ising lattice model as a testbed for improvement of theory of both homogeneous and heterogeneous nucleation theory. First we briefly overview the classical nucleation theory (CNT), and two typical simple systems on which simulations are performed - hard spheres, and Ising lattice model. Than we overview some results obtained by this approach and point to possible new directions of research and improvement.

Micro Layout Research of Reclamation Area Based on Plane Grid Topology Formation

The micro-layout research of the reclamation area involves many other areas and disciplines, occupies an important position in the coastal economic study. On the base of geometry theory, this paper puts the micro-layout of the reclamation area under the economic analysis within the formation of two-dimensional plane of the grid point topology. Here we take the Heishijiao coastal areas of Dalian as the example for micro layout of the reclamation area research within the two-dimensional plane variable framework, which is calculated by the Ising lattice model. For the better macroeconomic development in the area as the objective function, the maximum economic value will determine the optimal layout. The results show that, in coastal reclamation area it should not be paid too much notation to the width of the extension in the sea, and more reclamation area should be gathered to the city's prosperity zone reflected in the overall layout of layering.