Thermodynamics in the vicinity of a relativistic quantum critical point 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

We study the thermodynamics of the relativistic quantum O(N model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form P(T)=P(0)+N(T^3/c^2)\calF_N(\Delta/T)where cis the velocity of the excitations at the QCP and \Deltais a characteristic zero-temperature energy scale. Using both a large-Napproach to leading order and the nonperturbative...