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We investigate the two-dimensional $q=3$ and 4 Potts models with a variable interaction range by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges as expressed by the number $z$ of equivalent…

Two dimensional Potts model is a classical example where the symmetry of the order parameter controls the order of a phase transition: on a square lattice with nearest-neighbours interaction, when the number of states $q$ is less than or…

We study the two-dimensional Potts model on the square lattice in the presence of quenched random-bond impurities. For q>4 the first-order transitions of the pure model are softened due to the impurities, and we determine the resulting…

We study a possible deconfined quantum phase transition in a realistic model of a two-dimensional Shastry-Sutherland quantum magnet, using both numerical and field theoretic techniques. Using the infinite density matrix renormalization…

The Potts conformal field theory is an analytic continuation in the central charge of conformal field theory describing the critical two-dimensional $Q$-state Potts model. Four-point functions of the Potts conformal field theory are…

The ground-state phase diagram and quantum phase transitions (QPTs) in a spin-1 compass chain are investigated by the infinite time-evolving block decimation (iTEBD) method. Various phases are discerned by energy densities, spin…

Fidelity approach has been widely used to detect various types of quantum phase transitions, including some that are beyond the Landau symmetry breaking theory, in condensed matter models. However, challenges remain in locating the…

We consider the two-dimensional random bond $q$-state Potts model within the recently introduced exact framework of scale invariant scattering, exhibit the line of stable fixed points induced by disorder for arbitrarily large values of $q$,…

Two quantum spin models with bilinear-biquadratic exchange interactions are constructed on the checkerboard lattice. It is proved that, under certain sufficient conditions on the exchange parameters, their ground states consist of two…

We explore the situation of intertwined quantum phase transitions (IQPTs), for which a QPT involving a crossing of two configurations is accompanied by a shape evolution of each configuration with its own separate QPT. We demonstrate the…

We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-neighbor (J2) interactions. Using the tensor renormalization-group method augmented by higher-order singular value decompositions, we…

We study the magnetic field driven Quantum Phase Transition (QPT) in electrostatically gated superconducting LaTiO3/SrTiO3 interfaces. Through finite size scaling analysis, we show that it belongs to the (2+1)D XY model universality class.…

We define a multiparty entanglement measure, called generalized geometric measure, that can detect and quantify genuine multiparty entanglement for any number of parties. The quantum phase transitions in exactly solvable models like the…

The universality class of a phase transition is often determined by factors like dimensionality and inherent symmetry. We study the magnetic dipole system in which the ground-state symmetry and the underlying lattice structure are coupled…

We consider the critical behavior of the random q-state Potts model in the large-q limit with different types of disorder leading to either the nonfrustrated random ferromagnet regime or the frustrated spin glass regime. The model is…

This review is focused on various properties of quantum phase transitions (QPTs) in the Interacting Boson Model (IBM) of nuclear structure. The model in its infinite-size limit exhibits shape-phase transitions between spherical, deformed…

We investigate the influence of local decoherence on a symmetry-protected topological (SPT) phase of the two-dimensional (2D) cluster state. Mapping the 2D cluster state under decoherence to a classical spin model, we show a topological…

Magnetic frustration can lead to peculiar magnetic orderings that break a discrete symmetry of the lattice in addition to the fundamental magnetic symmetries (i.e., spin rotation invariance and time-reversal symmetry). In this work, we…

We show that for quantum phase transitions with a single bosonic zero mode at the critical point, like the Dicke model and the Lipkin-Meshkov-Glick model, metric quantities such as fidelity, that is, the overlap between two ground states…

We discuss quantum many-body systems with lattice translation and discrete onsite symmetries. We point out that, under a boundary condition twisted by a symmetry operation, there is an exact degeneracy of ground states if the unit cell…