  We evaluate the exact concurrence between any two spins in a cyclic XX chain
of n spins placed in a uniform transverse magnetic field, both at zero and
finite temperature, by means of the Jordan-Wigner transformation plus a number
parity projected statistics. It is shown that while at T=0 there is always
entanglement between any two spins in a narrow field interval before the
transition to the aligned state, at low but non-zero temperatures the
entanglement remains non-zero for arbitrarily high fields, for any pair
separation L, although its magnitude decreases exponentially with the field. It
is also demonstrated that all associated limit temperatures approach a constant
non-zero value in this limit, which decreases as 1/L^2 for L<<n but exhibit
special finite size effects for distant qubits (L approx. n/2). Related aspects
such as the different behavior of even and odd antiferromagnetic chains, the
existence of n ground state transitions and the thermodynamic limit are also
discussed.
