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Thermodynamics of dilute XX chain in a field

The isotropic spin one-half XY chain in transverse field (XX chain) has specific ground state phase with permanent criticality (quasi-long-range ordered, QLRO, phase) which exists in a field less than nearest-neighbor exchange. It is characterized by gapless excitations and power law decay of transverse correlators. The dilution of XX chain has drastic effect on this phase: the infinite series of quantum phase transitions marked by magnetization jumps appears in it. The thermodynamics of dilute XX chain allows exact analytical description revealing the peculiarities of the appearing transitions. We calculate the low-temperature magnetization, entropy, longitudinal magnetic susceptibility and specific heat of dilute model to elucidate the influence of quantum transitions on their field and low-temperature behavior. The changes of pair spin correlators under dilution are also analyzed. We argue that other dilute quantum spin chains and ladders with the gapless (algebraic) spin-liquid states would also exhibit the quantum jumps under variation of couplings and field similar to those of XX chain.