Seminar by Prof. Abhishodh Prakash

Abstract: Landau's theory gives us a remarkably successful local grammar for continuous phase transitions: identify the order parameter, its broken symmetries, and the relevant long-wavelength fluctuations. Over time, however, this success has hardened into several stronger assumptions. One is that every possible continuous transition belongs to Landau's paradigm of spontaneous symmetry breaking (SSB), with the unbroken symmetries of one phase forming a subset of those of the other. As a corollary, stable continuous transitions are often taken to necessarily separate distinct phases, in contrast to first-order transitions, which can terminate within a single phase, as in the liquid-gas transition.

The advent of quantum phases has challenged this paradigm in several ways. First, a wide range of "topological" phases have been discovered that are not classified by symmetry breaking. Second, direct transitions between Landau-incompatible SSB phases have been found, giving rise to the notion of "deconfined quantum criticality" (DQC). Third, it has been shown that stable critical surfaces can abruptly terminate, a phenomenon dubbed "unnecessary criticality." In each case, the quantum setting—through entanglement and Berry-phase effects—has seemingly played a crucial role.

I will argue that this is not the case, and demonstrate the existence of direct transitions between Landau-incompatible phases in a series of well-known classical statistical-mechanical models introduced by José, Kadanoff, Kirkpatrick, and Nelson (JKKN). Familiar DQC phenomenology, including the melting of charged defects and emergent symmetries that rotate between order parameters, appears naturally in these models. In a different regime of the same family of models, I will also demonstrate that stable critical surfaces can abruptly terminate.

This talk is based on existing [1,2] and upcoming joint work [3] with Nick Jones, Vishnu Pulloor Kuttanikkad, Rajesh Narayanan, and Titas Chanda.

[1] A. Prakash and N. G. Jones, "Classical Origins of Landau-Incompatible Transitions," Phys. Rev. Lett. 134, 097103 (2025).

[2] P. K. Vishnu, A. Prakash, R. Narayanan, and T. Chanda, "Two-Dimensional J1-J2 Clock Model: Enhanced Symmetries, Emergent Orders, and Landau-Incompatible Transitions," Phys. Rev. Lett. 135, 256703 (2025).

[3] T. Chanda and A. Prakash, "Stable Critical Surfaces Can Terminate in Classical Matter", in preparation.

Venue: Seminar Room (202), Physics Department IIT Bombay, Powai, Mumbai