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We present the detailed analysis of the spherical s+p spin glass model withtwo competing interactions: among p spins and among s spins. The mostinteresting case is the 2+p model with p > 3 for which a very rich phasediagram occurs, including, next to the paramagnetic and the glassy phaserepresented by the one step replica symmetry breaking ansatz typical of thespherical p-spin model, other two amorphous phases. Transitions between twocontiguous phases can also be of different kind. The model can thus serve asmean-field representation of amorphous-amorphous transitions (or transitionsbetween undercooled liquids of different structure). The model is analyticallysolvable everywhere in the phase space, even in the limit where the infinitereplica symmetry breaking ansatz is required to yield a thermodynamicallystable phase.Comment: 21 pages, 18 figure

physical review. b, condensed matter and materials physics

Spherical<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:mi>p</mml:mi></mml:mrow></mml:math>spin-glass model: An analytically solvable model with a glass-to-glass transition

Spherical2+pspin-glass model: An analytically solvable model with a glass-to-glass transition