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We study a cluster Ising model with non-Hermitian external field which can be exactly solved in the language of free fermions. By investigating the second derivative of energy density and fidelity, the possible new critical points are…
A coherent Ising machine (CIM) is known to deliver the low-energy states of the Ising model. Here, we investigate how well the CIM simulates the thermodynamic properties of a two-dimensional square-lattice Ising model. Assuming that the…
We present a new formalism for studying the topology of HII regions during the Epoch of Reionisation, based on persistent homology theory. With persistent homology, it is possible to follow the evolution of topological features over time.…
The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to…
Using quantum Monte Carlo simulations and field-theory arguments, we study the fully frustrated (Villain) transverse-field Ising model on the square lattice. We consider a "primary" spin order parameter and a "secondary" dimer order…
Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…
In this paper, we apply machine learning methods to study phase transitions in certain statistical mechanical models on the two dimensional lattices, whose transitions involve non-local or topological properties, including site and bond…
Optimum ground states are constructed in two dimensions by using so called vertex state models. These models are graphical generalizations of the well-known matrix product ground states for spin chains. On the hexagonal lattice we obtain a…
Persistent homology studies the birth and death of cycles in a parameterized family of spaces. In this paper, we study the birth and death of cycles in a multifiltration of a chain complex with the goal of producing a persistence diagram…
Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by…
Two-dimensional Ising models on the honeycomb lattice and the square lattice with striped random impurities are studied to obtain their phase diagrams. Assuming bimodal distributions of the random impurities where all the non-zero couplings…
We study a continuous quasi-two-dimensional order-disorder phase transition that occurs in a simple model of a material that is inhomogeneously strained due to the presence of dislocation lines. Performing Monte Carlo simulations of…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their…
We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems,…
Persistent homology is an important methodology in topological data analysis which adapts theory from algebraic topology to data settings. Computing persistent homology produces persistence diagrams, which have been successfully used in…
We investigate the processes of synchronization and phase ordering in a system of globally coupled maps possessing bistable, chaotic local dynamics. The stability boundaries of the synchronized states are determined on the space of…
Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the…
Experimental systems with a first order phase transition will often exhibit hysteresis when out of equilibrium. If defects are present, the hysteresis loop can have different shapes: with small disorder the hysteresis loop has a macroscopic…
We present a new method for the statistical process control of lattice structures using tools from Topological Data Analysis. Motivated by applications in additive manufacturing, such as aerospace components and biomedical implants, where…