Share your experience!
Is your phone's software up to date? Check it with PC companion. If there is an update available, update your phone. Also take a look at this FAQ page:
http://talk.sonymobile.com/t5/FAQ/Does-your-phone-feel-slow-and-laggy/m-p/347824#U347824
A few other users too have had your problem. Take a look at these pages too:
http://talk.sonymobile.com/t5/Xperia-J/Phone-hanging/m-p/290773#M756
http://talk.sonymobile.com/t5/Xperia-J/sony-xperia-j-lagging-so-badly/m-p/299739#M1117