Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

The U(1)symmetry of the X X Z central spin model with an arbitrary central magnetic field B is broken,since its total spin in the z-direction is not conserved.We obtain the exact solutions of the system by using the off-diagonal Bethe ansatz method.The thermodynamic limit is investigated based on the solutions.We find that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy satisfies an N^(-1)scaling law,where N is the total number of spins.This result makes it possible to investigate the properties of the system in the thermodynamic limit.By assuming the structural form of the Bethe roots in the thermodynamic limit,we obtain the contribution of the direction of B to the ground state energy.It is shown that the contribution of the direction of the central magnetic field is a finite value in the thermodynamic limit.This is the phenomenon caused by the U(1)symmetry breaking of the system.

Comment on 'Mathematical structure of the three-dimensional (3D) Ising model'

The review paper by Zhang Zhi-Dong （Zhang Z D 2013 Chin. Phys. B 22 030513, arXiv：1305.2956） contains many errors and is based on several earlier works that are equally wrong.

Analysis of the thermodynamic performance limits of the organic Rankine cycle in low and medium temperature heat source applications

In this paper,an exploration of the practical thermodynamic performance limits of the organic Rankine cycle(ORC)under working fluid and cycle parameter restrictions is presented.These performance limits are more realistic benchmarks for the thermodynamic cycle than the efficiency of the Carnot cycle.Subcritical ORC configuration with four typical case studies that are related to temperature ranging from 373.15 to 673.15 K is taken into account.The ORC is defined by its cycle parameters and working fluid characteristic properties.The cycle parameters involve evaporation temperature(T_(eva)),condensation temperature(T_(con))and superheat degree(ΔT_(sup)),while the working fluids are represented by the characteristic properties including critical temperature(T_(c)),critical pressure(p_(c)),acentric factor(ω),and molar ideal gas isobaric heat capacity based on the principle of corresponding states.Subsequently,Pareto optimum solutions for obtained hypothetical working fluids and cycle parameters are achieved using multi-objective optimization method with the consideration of both thermal efficiency(η_(th))and volumetric power output(VPO).Finally,sensitivity analysis of the working fluid characteristic properties is conducted,and the second law of thermodynamics analysis,especially the applicability of entropy generation minimization,is performed.The results show that the current commonly used working fluids are widely scattered below the Pareto front that represents the tradeoff betweenη_(th) and VPO for obtained hypothetical fluids.T_(eva) and T_(con) are the most dominant cycle parameters,while T_(c) and ωtend to be the most dominant characteristic property parameters.The entropy generation minimization does not give the same optimal results.