Temperature-Resistant Order in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> Dimensions

High temperatures are typically thought to increase disorder. Here we examine this idea in quantum field theory in 2+1 dimensions. For this sake we explore a novel class of tractable models, consisting of nearly-mean-field scalars interacting with critical scalars. We identify UV-complete, local, unitary models in this class and show that symmetry breaking Z_{2}→∅ occurs at any temperature in some regions of the phase diagram. This phenomenon, previously observed in models with fractional dimensions, or in the strict planar limits, or with nonlocal interactions, is now exhibited in a local, unitary 2+1 dimensional model with a finite number of fields.