Quantum spherical spin model on hypercubic lattices

We present an alternative treatment to the quantum spherical spin model on (d≥2) -dimensional hypercubic lattices, focusing on the effects of quantum (g) and thermal (T) fluctuations, under a uniform magnetic field h , on the correlation function, correlation length, entropy, specific heat, and energy gap in the excitation spectrum. Explicit expressions for such quantities are provided close to the d≥2 quantum ( g=g_c , T=0 ) and d≥3 thermal [T=T_c(g)] phase transitions in h=0 , including the low- T quantum regimes near the quantum critical point. In particular, the calculation of the correlation function and correlation length generalizes the results on the g=0 classical spherical model. At T=0 , the zero-field system is gapless at and below g_c ; however, a gap opens in the quantum-disordered ground state, g>g_c . Conversely, the null gap for T≤T_c(g≠0) becomes finite as T→T_c(g≠0)⁺ ; thus, quantum fluctuations suppress the critical prefactors of observables near T_c(g≠0) , though they are irrelevant to the universality class shared with the gapless classical spherical model. The results on the entropy and specific heat in g≠0 circumvent the drawback in classical spherical models concerning the third law of thermodynamics, as T→0 .