It seems the brand new Xperia Z is suffering from similar problems as the Xperia V, which was only released in December 2012. Is it possible then that either Sony is incapable of producing technically advanced phones that have been checked and work properly, free of bugs and battery problems? It certainly seems so.
Check out the problems with the Xperia V on the following link, particularly the 'Random freeze in Standby' issues, for which there is still no solution (finally now confirmed after over a month and a long-term campaign to force SOny to reply to its customers).
If you get no joy from Sony Mobile here then try 'direct messaging' then on the Sony Mobile Facebook page for your own country, and get a refernce number and the name of the person you speak to. Keep a record of all communication with the company.
If that doesn't work and Sony will not refund your money for another sub-standard product then I suggest you send a copy of everything to various Tech and mobile phone magazines and ask themn to take up the case for you. Sony will not do this as they wish to keep problems quiet (on here) and away from the attention of the public and media, so you may have to force their hand! Try things like GSM Arena, CNet, TechCrunch, What Mobile, Mobile Gazette, Mobile Choice, and any others you can find (do a search for 'mobile phones' on Twitter for instance).
Frankly I would insist on your money back if your phone does not work without problems. The Xperia Z is after all a new phone and Sony's flagship. Good luck... I think you are going to need it!
Xperia V - problems & issues page (some seem to be the same as the Z)
http://talk.sonymobile.com/community/support/xperia_v
