**April 2014**

**Physical Review Letters 112 (2014) 102002**

DOI: 10.1103/PhysRevLett.112.102002

### Universality and the QCD Anderson transition

**Matteo Giordano, Tamás G. Kovács and Ferenc Pittler**

Quarks are strongly interacting fundamental particles, they are the constituents of protons, neutrons and all other hadrons. Strongly interacting matter has two different phases: at low temperature it is in the hadronic phase, at high temperature it forms a quark-gluon plasma. It has been known for a long time that in the hadronic phase, quark states are delocalized compared to the correlation length of the system. Recently we discovered that in the high temperature, quark-gluon plasma phase the lowest quark states become localized whereas higher up in the spectrum, states remain delocalized. The transition from localized to delocalized states within the spectrum is reminiscent of the so called ``Anderson transition''.

Anderson transitions are well known in crystalline conductors with disorder. In that case due to the presence of impurities some of the states along the band edge can become localized and as a result, the zero temperature conductivity is lost if the Fermi level is in the domain of localized states. The Anderson transition is a second order phase transition characterized by a diverging correlation length at the critical point. The exponent describing this divergence is universal, independent of the details of the microscopic interactions.

In the present work we showed that the transition from localized to delocalized quark states becomes singular in the thermodynamic limit and it is characterized by the same critical exponent as the corresponding Anderson transition. This implies that the QCD transition is a genuine Anderson transition. All previously known Anderson transitions occured on atomic length and energy scales. It is remarkable that the QCD transition, characterized by vastly different energy and length scales, exhibits the same universal critical behavior.

Our result is based on high statistics lattice QCD simulations of systems of various spatial sizes. We used finite size scaling, a systematic study of how the transition becomes sharper as the volume of the system grows, to determine the critical exponent. The precision of our result is comparable to that of the best result in the literature for the Anderson model, the most widely studied model of Anderson transitions.

## Earlier:

**March 2014**

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J. Math. Phys. 54, 053502 (2013)

Coulomb-distorted plane wave: Partial wave expansion and asymptotic forms

J. Math. Phys. 54, 053502 (2013)

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**February 2014**

Electroweak measurements in electron-positron collisions at W-boson-pair energies at LEP

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**January 2014**

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**December 2013**

A neutron spectrometer for studying giant resonances with (p,n) reactions in inverse kinematics

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Volume 736 (2014) 1.

A neutron spectrometer for studying giant resonances with (p,n) reactions in inverse kinematics

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**November 2013**

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Physical Review Letters 111 (2013) 061104.

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and Á.Z. Kiss

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