The Spherical $$p+s$$ Spin Glass at Zero Temperature

Abstract We determine the structure of the Parisi measure at zero temperature for the spherical $$p+s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> spin glass model. We show that depending on the values of p and s , four scenarios may emerge, including the existence of 1-FRSB and 2-FRSB phases as predicted by Crisanti and Leuzzi (Private communication, 2022, Phys Rev B 73:014412, 2006). We also provide consequences for the model at low temperatures.