Phase transition in anisotropic holographic superfluids with arbitrary dynamical critical exponent z and hyperscaling violation factor $$\alpha $$ α
Abstract Einstein-scalar-U(2) gauge field theory is considered in a spacetime characterized by $$\alpha $$ α and z, which are the hyperscaling violation factor and the dynamical critical exponent, respectively. We consider a dual fluid system of such a gravity theory characterized by temperature T a...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-11-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-017-5382-8 |
| _version_ | 1828531559510048768 |
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| author | Miok Park Jiwon Park Jae-Hyuk Oh |
| author_facet | Miok Park Jiwon Park Jae-Hyuk Oh |
| author_sort | Miok Park |
| collection | DOAJ |
| description | Abstract Einstein-scalar-U(2) gauge field theory is considered in a spacetime characterized by $$\alpha $$ α and z, which are the hyperscaling violation factor and the dynamical critical exponent, respectively. We consider a dual fluid system of such a gravity theory characterized by temperature T and chemical potential $$\mu $$ μ . It turns out that there is a superfluid phase transition where a vector order parameter appears which breaks SO(3) global rotation symmetry of the dual fluid system when the chemical potential becomes a certain critical value. To study this system for arbitrary z and $$\alpha $$ α , we first apply Sturm–Liouville theory and estimate the upper bounds of the critical values of the chemical potential. We also employ a numerical method in the ranges of $$1 \le z \le 4$$ 1 ≤ z ≤ 4 and $$0 \le \alpha \le 4$$ 0 ≤ α ≤ 4 to check if the Sturm–Liouville method correctly estimates the critical values of the chemical potential. It turns out that the two methods are agreed within 10 percent error ranges. Finally, we compute free energy density of the dual fluid by using its gravity dual and check if the system shows phase transition at the critical values of the chemical potential $$\mu _\mathrm{c}$$ μ c for the given parameter region of $$\alpha $$ α and z. Interestingly, it is observed that the anisotropic phase is more favored than the isotropic phase for relatively small values of z and $$\alpha $$ α . However, for large values of z and $$\alpha $$ α , the anisotropic phase is not favored. |
| first_indexed | 2024-12-11T22:39:25Z |
| format | Article |
| id | doaj.art-5031e13a667b497b89c953fb0f28ab10 |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-11T22:39:25Z |
| publishDate | 2017-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-5031e13a667b497b89c953fb0f28ab102022-12-22T00:47:50ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522017-11-01771111210.1140/epjc/s10052-017-5382-8Phase transition in anisotropic holographic superfluids with arbitrary dynamical critical exponent z and hyperscaling violation factor $$\alpha $$ αMiok Park0Jiwon Park1Jae-Hyuk Oh2Korea Institute for Advanced StudyDepartment of Physics, Hanyang UniversityDepartment of Physics, Hanyang UniversityAbstract Einstein-scalar-U(2) gauge field theory is considered in a spacetime characterized by $$\alpha $$ α and z, which are the hyperscaling violation factor and the dynamical critical exponent, respectively. We consider a dual fluid system of such a gravity theory characterized by temperature T and chemical potential $$\mu $$ μ . It turns out that there is a superfluid phase transition where a vector order parameter appears which breaks SO(3) global rotation symmetry of the dual fluid system when the chemical potential becomes a certain critical value. To study this system for arbitrary z and $$\alpha $$ α , we first apply Sturm–Liouville theory and estimate the upper bounds of the critical values of the chemical potential. We also employ a numerical method in the ranges of $$1 \le z \le 4$$ 1 ≤ z ≤ 4 and $$0 \le \alpha \le 4$$ 0 ≤ α ≤ 4 to check if the Sturm–Liouville method correctly estimates the critical values of the chemical potential. It turns out that the two methods are agreed within 10 percent error ranges. Finally, we compute free energy density of the dual fluid by using its gravity dual and check if the system shows phase transition at the critical values of the chemical potential $$\mu _\mathrm{c}$$ μ c for the given parameter region of $$\alpha $$ α and z. Interestingly, it is observed that the anisotropic phase is more favored than the isotropic phase for relatively small values of z and $$\alpha $$ α . However, for large values of z and $$\alpha $$ α , the anisotropic phase is not favored.http://link.springer.com/article/10.1140/epjc/s10052-017-5382-8 |
| spellingShingle | Miok Park Jiwon Park Jae-Hyuk Oh Phase transition in anisotropic holographic superfluids with arbitrary dynamical critical exponent z and hyperscaling violation factor $$\alpha $$ α European Physical Journal C: Particles and Fields |
| title | Phase transition in anisotropic holographic superfluids with arbitrary dynamical critical exponent z and hyperscaling violation factor $$\alpha $$ α |
| title_full | Phase transition in anisotropic holographic superfluids with arbitrary dynamical critical exponent z and hyperscaling violation factor $$\alpha $$ α |
| title_fullStr | Phase transition in anisotropic holographic superfluids with arbitrary dynamical critical exponent z and hyperscaling violation factor $$\alpha $$ α |
| title_full_unstemmed | Phase transition in anisotropic holographic superfluids with arbitrary dynamical critical exponent z and hyperscaling violation factor $$\alpha $$ α |
| title_short | Phase transition in anisotropic holographic superfluids with arbitrary dynamical critical exponent z and hyperscaling violation factor $$\alpha $$ α |
| title_sort | phase transition in anisotropic holographic superfluids with arbitrary dynamical critical exponent z and hyperscaling violation factor alpha α |
| url | http://link.springer.com/article/10.1140/epjc/s10052-017-5382-8 |
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