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arXiv:1608.04424 · Physical review. B./Physical review. B

Constraints on the merging of the transition lines at the tricritical point in a wing-structure phase diagram

Valentin Taufour, Udhara S. Kaluarachchi, V. G. Kogan

Published Aug 19, 2016• 11 citations
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Abstract

We consider the phase diagram of a ferromagnetic system driven to a quantum phase transition with a tuning parameter $p$. Before being suppressed, the transition becomes of the first order at a tricritical point, from which wings emerge under application of the magnetic field $H$ in the $T\ensuremath{-}p\ensuremath{-}H$ phase diagram. We show that the edge of the wings merge with tangent slopes at the tricritical point.

DOI
10.1103/physrevb.94.060410

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We consider the phase diagram of a ferromagnetic system driven to a quantum phase transition with a tuning parameter ppp. Before being suppressed, the transition becomes of the first order at a tricritical point, from which wings emerge under application of the magnetic field HHH in the T\ensuremath−p\ensuremath−HT\ensuremath{-}p\ensuremath{-}HT\ensuremath−p\ensuremath−H phase diagram. We show that the edge of the wings merge with tangent slopes at the tricritical point.
We consider a phi4 theory with a position-dependent distance from the critical point. One realization of this model is a classical ferromagnet subject to nonuniform mechanical stress. We find a sharp phase transition where the envelope of the local magnetization vanishes uniformly. The first-order transition in a quantum ferromagnet also remains sharp. The universal mechanism leading to a tricritical point in an itinerant quantum ferromagnet is suppressed, and in principle, one can recover a quantum critical point with mean-field exponents. Observable consequences of these results are discussed.
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We describe the quantum phase transitions in the ferromagnetic Dicke-Ising model using a Landau theory approach. The theory quantitatively captures the change from a second- to a first-order transition between the normal and superradiant phases through a tricritical point. We identify virtual nearest-neighbor double spin-flip processes as the crucial mechanism responsible for this behavior. The tricritical point constitutes a quantum phase transition above the upper critical dimension. We discuss the modifications to finite-size scaling required for the correct interpretation of numerical data at the tricritical point. Our results emphasize the need for adapted finite-size scaling forms in all-to-all interacting quantum systems and establish the ferromagnetic Dicke-Ising model as a paradigmatic platform for quantum phase transitions above the upper critical dimension, encompassing both standard φ4φ^4φ4 criticality and beyond.