Fig. 1. (color online) Hedgehog profiles for various values of the isospin chemical potential . The profiles are the exact solutions of Eq. (8) except the gray dashed curve. The red solid curve represents the solution for the isospin chemical potential , the blue dot-dashed curve is for , and the yellow dotted curve for . The gray dashed curve, which behaves as a spherical Bessel function at large distances, is for , which is larger than the critical isospin chemical potential , but is not a soliton solution which has localized finite energy. It is clearly seen that the isospin chemical potential has a distinct influence on the profile when

Fig. 2. (color online) The soliton mass as a function of the isospin chemical potential for the spherically symmetric hedgehog ansatz. For , the soliton mass is almost stable, while for the soliton mass decreases with the increase of the isospin chemical potential. The curve stops at , which is close to .

Fig. 3. (color online) as a function of . For the isospin chemical potential , the rms radius (the blue solid curve) diverges, which suggests the occurrence of a phase transition.

Fig. 4. (color online) as a function of . For isospin chemical potential larger than , the rms radius diverges.

Fig. 5. (color online) The baryon number density as a function of for typical values of the isospin chemical potential. The red solid curve is for the isospin chemical potential , the blue dot-dashed curve for , and the purple dashed curve for .

Fig. 6. (color online) The skyrmion thermal profile F as a function of at finite temperature and zero isospin chemical potential. The red solid curve is for the temperature , the blue dashed curve for , and the purple dotted curve for . Note that is the critical temperature when the isospin chemical potential is zero.

Fig. 7. (color online) The soliton mass as a function of in the spherically symmetric hedgehog ansatz and for . The blue solid curve is the soliton mass for ( MeV); the minimum ( MeV) is at . The orange dashed curve is for ( MeV) with the minimum at . The green dot-dashed line is for the critical temperature ( = MeV) where the minimum does not exist.

Fig. 8. (color online) The dependence of the critical temperature on the isospin chemical potential in the spherically symmetric hedgehog ansatz.